I hate hot weather. I hate it so much more than I hate when it's cold, because even though I feel like the Michelin Man, being in the cold means that I can always put on another layer. And if I really think about it, the reason why I hate the cold is because when I'm warm enough to be comfortable outside, I'll be burning hot inside. Don't get me wrong, I love a sunny day just as much as the next guy. But forget about the raging infernos and the pits of fire, being in a room that's 28+ Celsius with zero draft is pretty much hell for me. The worst thing about the heat is not the physical discomfort, but rather, it's the apparently debilitating effect it has on my cognitive functions, which lead me to ask: what exactly it is about the heat that fucks up my day?
I can understand how general physical discomfort can piss off the brain enough till it stop functioning. But instead of lumping this cause & effect, we can be a bit more scientific about it and focus on the heat for the moment, and consider a few explanations that are as orthogonal as possible. As always, I assume that I'm not some alien life form on Earth and that other people experience similar distaste for this suffocating heat.
Broadly speaking, we can look at how the heat gets to your head in two ways: direct vs. indirect. By direct mechanism I am referring to the temperature dependence of neurons and cell function in general, which should be rather straightforward to study, such as the ionic equilibrium potential, governed by the Nernst equation. There is probably a very fine temperature range, outside of which abnormal cell states begin to manifest. However, this will most likely turn out to have a minute effect, since the human body is so adept at regulating its internal temperature. It should be noted here that this is assuming that I am capable of normal thermoregulation, since in pathological situations such as a high fever, even a few degrees can cause permanent brain damage . Interestingly, nerve conduction speed, which I will take as a first order approximation for regular cognitive processes, sees an increase proportional to temperature . This means that to some degree, you might actually be smarter and/or faster when it gets hot! Not really, but the point of all of this is that this level of heat (< 40C) probably won't affect your neurons all that much, and for the amount of heat that does get through, it won't actually make you stupid on a cellular level.
Scratch that,  shows overall increased cognitive performance with slightly increased body temperature, controlling for factors such as circadian rhythm, hours awake, etc. I haven't gone into the details too much, one of my biggest question being the effectiveness of their attempt to control for sleep. But this is really starting to hurt my case either way.
The other possibility, then, is by ways of an indirect mechanism, perhaps a side effect of the regular thermoregulation process. Speaking from my own experience, aside from being incredibly slow, two of the more prevalent effects of a hot day are irritability and lack of motivation, i.e. I become a crank couch potato. A quick scan at literature reveals that this exact effect has indeed been shown:  notes self-reported increase in irritability and decrease in alertness, but curiously, also improved speeds at math calculation and verbal reasoning, with a 2 degree Celsius increase in body temperature;  notes increased preference for aggression-type activity, although this one comes with a huge caveat, and frankly the experiment design itself is pretty hilarious, so give that a read. Finally,  summarizes a few other studies, looking at a positive correlation between warm temperature and mood, suicide, and violent crimes.
All in all, what I've managed to learn through this little excursion is that 1) people hate hot and humid temperatures, 2) cognitive performance does not actually suffer with increased temperature, and 3) this needs more research to draw conclusive findings. In essence, it's all in my head. A few notes to consider, however: first, the cognitive tasks performed in the studies are usually straightforward and mechanical, i.e. calculations and reading comprehension. This limits the proficiency findings to only a subset of tasks, and not others, such as more open tasks like writing (I know I had a lot of trouble finishing up this piece in this suddenly >25 C weather). Second, motivation was essentially a non-issue in these tasks, because it isn't really up to the participants to push themselves to do the task, unlike in real-life situations at home or work. Third, I really need to get AC in the house. Finally, although I didn't find a satisfactory answer, we can venture a guess as to why both the laziness and the irritability come about: due to the already high ambient temperature, the body probably wants no part in extra movements that will generate even more body heat, thus reducing me to a potato; and as for irritability, it might be a product of all the pent up energy the body doesn't need to use for heating anymore.
Basically, I'm too hot to move, but already hot enough to be pissed.
My citation formatting is really going out the window. Thank god for automatic citation.
 Fever. MedlinePlus. Updated: May 16, 2014. Accessed: May 27, 2014. http://www.nlm.nih.gov/medlineplus/ency/article/003090.htm
 Matthew C. Kiernan et al. Effects of temperature on the excitability properties of human motor axons. Brain (2001) 124 (4): 816-825 doi:10.1093/brain/124.4.816
 Kenneth P. Wright et al. Relationship between alertness, performance, and body temperature in humans. American Journal of Physiology - Regulatory, Integrative and Comparative Physiology. Dec 2002,283(6)R1370-R1377; DOI:10.1152/ajpregu.00205.2002
 R. L. Holland et al. Effects of raised body temperature on reasoning, memory, and mood. Journal of Applied Physiology. Dec 1985,59(6)1823-1827;
 D.L. Palamarek & B.G. Rule. The effects of ambient temperature and insult on the motivation to retaliate or escape. Motivation and Emotion. Mar 1979, Volume 3 Issue 1, pp 83-92