Interesting.
I posted the same observation not long ago, but got somewhat different answers.
I think some of the responders are confused by the way you phrased it. When you say the boiler temperature is set to 200F, that's really the boiler temperature minus the offset (i.e., the target brew or group temperature.) If the Scace rises to 205F during the shot, it's likely that the offset is programmed at about 5-6 degrees.
This isn't about the offset being wrong or your Fluke not being calibrated. It's about the GS/3 temperature profile during a shot.
My Scace shows that the temperature at the group increases 3-4 degrees after starting the shot, then stabilizes, just like yours (and, yeah, I set the digital thermometer for a type T thermocouple and calibrated over a steam bath.) For example, if I target a brew temperature of 196.5F, then I must set the boiler temperature to 200.5F. That's because LM programmed my machine with a temperature offset of 4F. When I run the shot, the Scace reading starts out at 196.5F, but quickly ramps up to about 200F.
Greg is correct that the water temperature in the boiler is higher than at the group head, presumably because the group head sticks out in space and there's less thermal mass to keep the water at the same temperature (i.e., heat dissipates more easily from the group head than the boiler.) That's why the temperature offset exists: it's designed to more or less accurately show you the temperature of the water in the group head, taking the heat loss into account.
Here's what I think is the explanation: When you start brewing, the cooler water that's resting in the group flows through the gicleur into the 3-way valve and thence through the TL30 tube to the dispersion block and puck. That's why initially you see the target temperature. But at the same time, hotter water flows into the group head from the boiler, raising the temperature of the water in the group. The gicleur (intake) is positioned at the back of the group head, close to the opening into the boiler, so the water around it is heated quickly. I suspect that the cooling effect of the group head isn't instantaneous, especially back near the boiler, nor is the cooling that takes place during the trip through the gicleur, 3-way and TL30. I think this is why the Scace shows the exit water ramping up 3-4 degrees. I would speculate that with +4F water flowing continuously into the group head over a 30 second period, there isn't time for the excess heat to be lost, and that's why we see stabilization at higher temperatures. I suppose there might be some counteracting effect of cold water flowing into the brew boiler (the temperature there usually drops .5F or so during a shot), but remember that the intake water is pre-warmed via heat exchange in the steam boiler, and the PID is working hard to keep the brew boiler at the temperature you set.
Going back to what Greg said, while it's true that the water won't be higher in the group than it is in the boiler, it most certainly is possible for hotter water from the boiler to flow into the group and raise the temperature of the water that's already there.
[NB, it would be interesting to see a temperature profile on a Speedster. The gicleur is way out near the dispersion block, so maybe the water temperature doesn't rise as much.]
I would think LM knows all this. So why do they bother having an offset that shows only the resting temperature of the group and not the actual brew temperature? Perhaps it's because the actual brew temperature is an average of the temperature curve throughout the shot, so it's neither the starting nor maximum/stabilized temperature during the shot. Hard to say exactly what the temperature is, isn't it?
I have no explanation for EricC's claim that the Scace readings are spot-on, presumably meaning that the temperature stays at the target value (i.e., brew boiler temperature minus the offset) throughout the shot. Frankly, given the geometry of the group head and water flow, I don't see how this is possible. But I'm just an amateur at this.
Focusing on the fact that we both see a rise in temperature, what does this mean? If the roaster recommends a brew temperature of 200F, does that really mean the water hitting the puck has to be 200F, or are they using a similar LM machine (likely in many cases) and they're simply reporting the target temperature they set on the machine (i.e., they're actually brewing several degrees higher)?
The best advice I got was to treat the temperature as relative. Use the roaster's/reviewer's recommendation as a starting point and adjust the temperature for best taste. That's what people who don't have LM machines have to do anyway. I could lower my offset to 0-1 degree, to better report the temperature that will prevail at the puck during most of the brew cycle, but since it's unlikely roasters or other GS3/LM owners do this, the information wouldn't be particularly useful. In other words, regardless of what the offset means, it's likely that LM uses the same procedure to set it on all their machines, establishing a common reference that makes it possible for LM owners to share temperature information.
The good news is that no matter what approach you take, the saturated group makes the temperature curve predictable, stable and reproducible, which is the most important thing for finding the right temperature and using it to consistently produce the same shot profile.