malachi wrote:As hinted at above...
If you're running a PID controlled machine or the like (indicating that you're really interested in temperature accuracy), insulating the boiler is likely to decrease the effectiveness of the control. So I'd suggest that (even if you run the machine 24/7) insulating your boiler is going to likely save you money at the cost of odds of consistent quality of espresso.
As someone who has actually done the above, I guess I would take issue with that.
I own 2 PID'd Cimbali Juniors of different vintages, as I have previously posted ad nauseum

The newer one, roughly 5 years old, is a plumbed in rotary "D" version, which came from the factory with an insulation blanket wrapped circumferentially around the boiler (but not covering the sides). The other machine, a 13 year old pourover "S" model, which I've completely plumbed in, was not sold with any boiler insulation.
Several years ago I insulated the boiler myself, with insulating wrap, secured with high temperature metal tape and supporting wires:

Three weeks ago I ran (yet another) calibration set of random walk-up Scace shots through this machine, using the boiler temperature I most frequently use, in order to get a shot temp of roughly 198F. I compared the static pre-shot grouphead adapter temperatures I got from Eric's grouphead adapter. As you can see, the static grouphead adapter temperature does have some impact on shot temperature.

I do not have any shot curves I can trust taken with this machine before I insulated its boiler for comparison. I would say, however, that if the boiler insulation has effected my shot temperature consistency, it sure hasn't done it to a significant extent.
The one thing that DOES markedly effect my shot temperature consistency is large variation in ambient room temperature, which my machines experience during a couple of months each year during the summer (I have no air conditioning and rely on opening the windows; there can be an indoor temperature swing of more than 20 degrees F. during this time period). I don't think that having the boiler insulated has any great impact on this phenomenon, one way or the other.
While I do think that insulating the boiler probably does lead to modest temperature overshoot in a PID'd machine, I would submit that the observed decrement in shot temperature consistency is not likely to be noticed by (approximately) 99.999% of the human population.
ken