Re: When to chronograph?
I've been doing a couple strings of 10, just to be sure at least two 10-shot strings are comparable. I usually try to do 4 x 5-shots groups at the same time for determining precision/group spreads with that particular ammo @ 100 yd.
I have a Chrony Beta Master (definitely <span style="font-style: italic">not</span> the highest end unit available) and 10 shots is the max for one string. After 10 shots, it starts replacing previous values in the string with new, so doing more than 10 shots doesn't improve the results. You may want to check how your chronograph actually records data strings to help you make an informed decision on how many shots to record.
As far as temp. effects, a lot will depend on the temperature-sensitivity the powder/load you're using (apparently some are more sensitive than others). I chrono'd some different factory loads (Black Hills and FGMM 168s/175s) on numerous different occasions throughout the last 6 months here in Nebraska, at temps ranging from low 20s (Dec/Jan) to upper 60s/low 70s (last week). I have seen very little change in MV (same weapon) over that temp range with those factory loads. However, YMMV, so you probably want to test/record the data just to be sure. That way, you will have the actual MV data with your specific weapon and load(s) at a few different temps, then you'll know for sure.
One other thing to keep in mind is that if your drops change noticeably between range trips, it is likely because your MV is changing. It's not the most accurate measurement, but can suggest changes in MV due to different atmospheric conditions such as temp, humidity, etc. So keeping good records of elevation correction necessary for a given distance on each range trip can also help as an indicator of changes in MV.
