One class of variance in cognitive test results is probably, effectively, pseudorandomness.
Suppose there’s a problem, and there are five plausible solutions you might try, two of which will work. Then your performance is effectively determined by the order in which you end up trying solutions. And if your skills and knowledge don’t give you a strong reason to prefer any of them, then it’ll presumably be determined in a pseudorandom way: whichever comes to mind first. Maybe being cold subconsciously reminds you of when you were thinking about stuff connected to Solution B, or discourages you from thinking about Solution C. Thus, you could get a reliably reproducible result that temperature affects your performance on a given test, even if it has no “real” effect on how well your mind works and wouldn’t generalize to other tests.
This should be addressable by simply taking more, different, cognitive tests to confirm any effect you think you’ve found.
I had heard, 15+ years ago (visiting neuroscience exhibits somewhere), about experiments involving people who, due to brain damage, can no longer form new memories. And Wiki agrees with what I remember hearing about some cases: that, although they couldn’t remember any new events, if you had them practice a skill, they would get good at it, and on future occasions would remain good at it (despite not remembering having learned it). I’d heard that an exception was that they couldn’t get good at Tetris.
Takeaway: “Memory” is not a uniform thing, and things that disrupt memory don’t necessarily disrupt all of it. So beware of that in any such testing. In fact, given some technique that purportedly blocks memory formation, “Exactly what memory does it block?” is a primary thing to investigate.