Espresso and milk, they're natural friends, right? Certainly that's true for our palates, but as fate would have it, they don't have an all too friendly relationship in terms of their preparation. To state the obvious, this is because espresso is brewed at one temperature and milk is frothed at a much higher one. This simple fact reveals the puzzle at the root of the espresso machine designer's dilemma: How to deliver these two vital components reliably and quickly? It becomes all the more difficult because espresso demands of temperature control (the initial temperature of the brew water) and temperature stability (the temperature of the brew water during the shot) are surprisingly exacting.
The video below explains the differences between two common types of boilers for high-end espresso machines, heat exchanger and double boilers:
From Heat Exchanger vs. Double Boiler Espresso Machines
The remainder of this post briefly introduces the three types of espresso machine designs:
Single boiler

This type of espresso machine has two temperature settings controlled by a pushbutton. When released, the brew thermostat controls the boiler temperature. When pressed in, the steam thermostat controls the boiler temperature. Since the boiler serves both purposes of brewing and steaming, you must wait while it transitions from brew to steam temperature.
Single boiler, heat exchanger

This type of espresso machine has a creative solution to the two-temperature problem: The boiler is kept partially filled to allow for a layer of steam. Since the water is under pressure, its boiling point is higher, just like in an old-fashioned pressure cooker. A copper tube passing through the boiler called a "heat exchanger" is responsible for flash heating fresh water from the reservoir to near final brew temperature. But how does it deliver the desired temperature with any hope of accuracy? This requires a little understanding of the underlying design of the E61 brew group and how its temperature is affected when coupled with a heat exchanger. Let's cover the essentials and see how this affects your preparation routine.
A popular brew group design is called the E61 (presumably owing to the year the patent was granted, the year of an eclipse). One of this design's unique contributions to temperature control and stability is the way it circulates hot water through the group, relying on the natural rise in water as it warms. If you've ever swam in a lake or pool at night, you have surely noticed that the top layer of water is much warmer than the layers below. This group takes advantage of this law of physics in order to circulate water from the boiler towards the grouphead. The water heats the group and cools, returning to the bottom of the boiler and the cycle repeats.
Weighing nine pounds and made of solid brass, this group delivers temperature stability the old fashioned way: By way of overwhelming thermal mass. Temperature-wise, think of the E61 brew group as a bowling ball and the few ounces of water for an espresso as an egg. Get all that solid brass to the desired brew temperature and we won't need a physicist to know what the water's final temperature will be. Got the picture?
However that's only part of the story. The rest involves the heat exchanger. When making espresso with a single boiler espresso machine like the one described earlier, there's no need for a heat exchanger since the boiler water is already at the appropriate brew temperature. For those who only make espresso, life can't be much easier. As was mentioned earlier, the problem begins when you want to quickly prepare two things requiring two different temperatures of water, namely espresso and frothed milk.

Read about the E61 patent and see the detailed interior schematics
Remember the natural circulation of the E61's thermosyphon? Alas, this is where conundrum begins: In a heat exchanger espresso machine, this system will circulate steam temperature water (~257F) through the group, not brew temperature water (~202F). Given enough time, the flash-heated water that ultimately arrives from the heat exchanger brew group will be considerably hotter than brew temperature, despite the dampening effect of the brass grouphead.
Thus the heat exchanger / E61 combination requires a "cooling flush" to reduce the temperature of the group to a more reasonable brew temperature. A natural question you might ask yourself is, "How much water is needed to cool the brew group?" The short answer is somewhere between four and six ounces, maybe a little more, and probably not less. Most home baristas apply a simple trial-and-error approach to judge if the cool down flush was correct by first drawing water through the group until the steam and sputtering subsides and then tasting the subsequent shot. If the espresso is sour, too much water was flushed, if it is bitter, too little was flushed. The good news is that once you've done the initial cool down flush, you can pull shot after shot of espresso at a reasonable pace and get good temperature control and stability. If the machine is idle for several minutes do you need to repeat the cool down flush (see How I Stopped Worrying and Learned to Love HXs for more details). The boiler temperature is controlled via a pressurestat; it allows the boiler pressure to drop 0.2 bar before it activates the heating element. That represents a temperature swing of only 4F.
The heat-exchanger system is efficient and with a little practice and attention to detail, delivers excellent temperature control. The E61 design is time-tested and widely recognized as one of the hallmarks of great espresso machines. However, of the three machines represented in this introduction, the heat exchanger espresso machine requires more attention to proper operation in order to produce an ideal espresso, however it isn't difficult to get the hang of the routine. If you wish to really refine your barista skills, there is of course abundant help and suggestions on the Internet.
One other point about the E61 design worth noting: It includes a preinfusion feature that can improve the quality of the extraction by allowing the pressure to build more slowly in the beginning of the pull. This slower build-up gives the puck a chance to expand and thereby reduce the occurrence of fissures that would otherwise lead to channeling. Channeling is the quick passage of water through the coffee, which produces a thinner, under-extracted espresso. When it occurs, you'll usually see sudden appearances of blond streaks in the stream of espresso and sometimes even pencil-sized holes in the coffee puck. The E61 has a reputation for being more "forgiving" because its preinfusion helps reduce the occurrences of channeling.
The E61 also allows for the diversion of some of the initial higher-temperature water away from the puck. The preinfusion and initial high-temperature water diversion are accomplished with the help of a small chamber located directly below the grouphead. If you are looking directly at the machine, it is the long silver cylinder below where the lever that engages the pump attaches. When the lever is in the up position, the pump starts and fills the grouphead. A spring-loaded valve leading to the preinfusion chamber allows a portion of the initial water to enter and thus reduces the overall pressure to around 4-6 bar until the chamber fills. Once this chamber is filled, the pressure raises to the full nine bar for the duration of the shot.
Double boiler

This type of espresso machine has separate boilers dedicated to each purpose and of course independent temperature controls. The particulars of the boiler and group design sometimes differs among double boilers. For example, the brew group design of the La Spaziale S1 has the grouphead directly attached to the boiler so heat transfer is via direct conduction, not water circulation as with the E61 brew group. Since the boiler is at brew temperature and it is an integral part of the group, the grouphead never overheats as is the case with the E61 / heat exchanger combination. The grouphead and portafilter may require a couple of blank shots, however, to bring them up to the final brew temperature. Otherwise the first and second shot will be cool by a few degrees.