Why does the predator only come in the hottest seasons?

This is a very open question. There are many explanations for this.

The old ones in the village cross themselves and whisper crazy things. "Demonio. Cazador de trofoes." Only the hottest times of the hottest years...

This is a very weak source.

• Maybe they only noticed the Predator during summer, because they wouldn't go on extended forest walks in winter.
• Since hardly anyone would go on extended forest walks in winter, that may simply preclude Predator from having a worthy prey to hunt during winter. If the people of that village e.g. only go hunting during summer, that means that Predator would only encounter an armed prey during summer. Note that the initial movie strongly suggested that Predator picks off the aggressive prey. It may consider unarmed targets to be too easy to hunt.
• Maybe they just randomly happened to encounter Predator during warm seasons, even if they were there in every season. E.g. what if the "shimmer" of a cloaked Predator is only noticeable in warm and/or well lit conditions?
• Maybe it's dramatic flavor, stemming from calling them demons, thus suggesting Hell and a hot environment.

If we assume all Predator movies to be canon, then Predator vs Alien established that Predators built a specific hunting grounds under the ice in Antarctica, thus suggesting that they are not in any way averse to the cold.

That would be consistent with elite hunters that try to handicap their advantages over their prey.

IIRC, the whole point of Predator coming to Earth is that it is a rite of passage for the unproven hunters. The Predators we encounter on Earth are rookies who are trying to pass their first trial. They are not elite hunters, and are likely honorbound (i.e. not hunting unarmed prey) but not necessarily trying to handicap themselves.

I'm trying to reconcile that with the fact that the movie appears to show the predator's vision is primarily in the thermal spectrum. Which would make detecting (and hunting) warm-blooded humans particularly difficult when ambient conditions are close to their body temperature.

We also don't know if Predator always uses heat vision, or only when they choose to. Since we see them hunt humans, it makes sense to want to use thermal vision to track them.

But to what extent does the predator-point-of-view cinematography and special effects reflect the intended visual capabilities of the predator?

We can't confirm this, but the visual highly suggest that we are seeing the HUD that Predator sees through its helmet. We see an intentional switching between camera modes (based on what's best in context), and intelligent tracking of targets.

1. The predator chooses to hunt in hot seasons, when thermal vision would be a handicap (right?)
2. But the predator wears a helmet that enhances thermal contrast, offsetting that handicap.

Less effective is not the same as a handicap. As there is no real proof that Predator seeks out hotter environments, there is no basis to assuming that Predator intentionally tries to make their thermal vision less effective.

And again, it's perfectly possible that Predator would have used a different tracking mode if it was actually impossible to use thermal vision. Seeing Predator use thermal vision may already be implicit confirmation that it was the best way to track humans at the time.

3. But for the final showdown, the predator removes its helmet and ... its unaided vision is terribly impaired in those conditions?

I'm not quite sure what your question is here.

Predator is clearly from a warrior culture. They are honor-bound (tend to not focus on unarmed prey, paid respect to the female protagonist in AVP when she saved Predator's life and showed prowess as a hunter) and prove themselves through combat (= rite of passage involving hunting worthy prey).

Dutch was not actively attacking Predator (and IIRC even unarmed) at the time Predator decided to remove his helmet. Going by most warrior cultures, it is dishonorable (or at least not honorable) to kill a prey who does not resist you (or is comparatively unarmed). But by removing his helmet, Predator removed his advantage over Dutch and leveled the playing field, thus making the kill more honorable.

Speculative answers inspired by Flater's:

I was assuming that Anna meant the predator only comes to hunt during the hottest seasons. But her halting and limited recollection of village legends is consistent with another interpretation: They are only able to see the predator during the hottest seasons.

Indeed, even before its camouflage begins to fail after being damaged by water and then explosions we see that during the exceptionally hot conditions in which the movie takes place:

1. The predator isn't fully invisible. Its ability to warp light might be degraded by heat and humidity.

2. The predator's helmet (for whatever reason) at various points emits green light from its eyes, making it look quite demonic.

It is noteworthy that the villagers weren't just finding dead men skinned like game. They understand that an inhuman "demon" and trophy hunter (as opposed to some wild animal) is the one doing it.

As for why the predator takes off its helmet to fight Dutch: It could be a matter of "honor:" I.e., initially it was just on a training and/or trophy hunt, but now it feels like it has been so challenged it has to prove itself. But it could also be that its gear was failing. Or it was just angry that Dutch had found a way to hide from the helmet's thermal vision, and so it was basically saying, "OK, you tricked my gear. Well I'm going to show you I don't need my gear to kill you."

Well, since the Movie Alien vs. Predator from 2004 is set in the Antarctic, I don't think they are necessarily limiting themselves to the warmest climate. So the crazy things the old ones in the village whisper might be just that: crazy.