Lots of very good info in all of the above posts, to which I don't disagree with any (not to mention that my specialty is not dimensional - although I have been in the business nearly 30 years).
The temperature issue with calibration of calipers is more an uncertainty issue (as the coefficient of expansion for your gage blocks comes into play). A legitimate method if calibrating away from 20 Deg C (68 Deg F) is to apply coefficients. HOWEVER, if that temp is away from 20 Deg C, I am guessing temperature stability is not good either. Therefore, since expansion and contraction of the gage blocks takes some period of time (one of you dimensional experts can fill in better on this), and IF your temp fluctuates, there is an increase in the instability of the actual value of each block.
Therefore, in such an environment, you may expect fluctuations in the actual performance of your gage blocks, and fluctuations in your calibrated readings (away from the true nominal). Using 68 Deg F as a reference temp for calibrations was established to improve the uncertainty of the calibrations. You might consider TRYING to achieve as close to 68 Deg F as possible even if your spec allows the deviation. In a lab where I used to work, we had a looser spec, but the dimensional guy surveyed and found the coldest spot in the room. He does the dimensional work there.
I don't believe matching the operating environment of the calipers is necessarily beneficial UNLESS there is a very predictable operational environment. For example, if they are alway used at 85 Deg F, calibrating them at 85 Deg F (including applying the coefficient to account for gage block expansion -- a miust) may potentially provide better calibration results. Problem is, because the calipers and gage blocks were designed around the 68 Deg F context, you may find readings are always a little skewed.
Again, you experts chime in on the following.... Am I correct the coefficients on ceramic blocks are better for unstable environments? If so, you may want to consider a different type block.
Okay. I haven't posted in a while and wanted to chime in about something. Have a great weekend everyone, and I hope I added some value to the discussion.