The snowy tree cricket's chirp does, in fact, vary with ambient temperature.
(Although, the number of chirps I counted would mean Sheldon's apartment is about 50 degrees. Which doesn't really bother me, because the writers got the basic science correct. Even if they flubbed it on the sound effect).~T = C+40where
~T is the approximate temperature in Fahrenheit
C is number of chirps in a 13 second interval
The mistake Sheldon made was in an inadequate test for his hypothesis. To properly discount the possibility of the common field cricket, Sheldon needed additional data. Namely, he needed to (at the very least) change the ambient air temperature of the room and observe whether the number of chirps per second changed by an appropriate margin before he made any determination. If the chirps changed, it could likely be a snowy tree cricket. If the chirps remain constant, it is not a snowy tree cricket. If the chirps changed, but not according to the known relationship, it is inconclusive.
It seems, from my perspective, that the writers compared/contrasted how the public perceives science to function and how it actually functions. The public perception was portrayed by Sheldon's haphazard application of a factoid of science. The actual process of science was portrayed by Howard challenging Sheldon to provide sufficient data to make such a claim. The public perception of science seems to be centered on science as a body of facts, rather than science as a crucible for reality. All too often, scientists are portrayed as dictating what is reality. When in actuality, scientists are only constantly coming up with tests to disprove (or add further support) some notion of what reality is.
One small gripe with the episode. Once they caught the cricket, the game was over. The two types of cricket don't look anything like each other. Jiminy the Snowy Tree Cricket:And Toby the Field Cricket:I really enjoy this show overall, and I think it is (generally) a good spokesman for science. I am glad that Sheldon was called on his poor methods (and ended up losing the bet). Hopefully, this subtle display about the scientific method, and the importance of peer review, is appreciated by the public consciousness.