Is there any link between educational testing scores and temperature,
heat or air conditioning

There is some evidence suggesting that there is a link between the two.

It also seems that the humidity of the testing room is another factor
to determine how well one may perform.

Here is an interesting essay that attempts to shed some light on this subject:
http://www.freeessays.cc/db/39/pnl97.shtml

On this very topic: "...though variation of more than 4°C in core body
temperature will impair physical and mental ability (Ramsey, 1983)."
-- You can find the whole lecture here:
  Human Performance, Lecture 7: Temperature and Performance.
  - http://psychology.unn.ac.uk/nick/HPlec07.htm

And if you would like a quick summary of exact numbers, see this brief:
  The effects of ambient temperature on cognitive performance.
  - http://www.lboro.ac.uk/departments/hu/projects/abstracts/03hb0032.html

Hope this helps!
-Krimson