It's important to know what a battle may have actually looked like in regards to this question. In this thread we have a rundown of a typical battle by /u/Hergrim:

https://www.reddit.com/r/AskHistorians/comments/7j6m6t/the_effectiveness_of_hand_to_hand_combat_or_how/dr4pkjr/?context=3

the typically medieval infantry battle probably went something like this: The two lines approached each other as fast as possible while still maintaining a reasonable amount of cohesion. Gradually, the two lines would slacken in pace until they were within throwing range of javelins or archery range. This this point they would attempt to use missile fire to break the enemy lines or open gaps they could exploit. If this failed to rout the enemy, they would move in to spear. It's possible that there would be an initial rush to try and break the enemy line. However, if this occurred, it would not last for long and both sides would withdraw to spear range by mutual consent and begin trying to stab over or under the shield of the men opposite them. While othismos - a shoving match between the two sides of a battle - may or may not have been an important part of Ancient Greek infantry battles, it could not have been a major part of medieval battles. Medieval shields are not designed in a way that would support this, and any attempt would likely suffocate most of the men involved. From here, the battle would proceed with each side stabbing at the other, occasionally making a push or close range attack on the other line in the hope of breaking it, pulling back by mutual consent when the sides became too tired by the combination of fear and physical exertion to continue fighting for the moment, then coming back together for the fencing or for a closer range attack. Spears will inevitably break, and men will be forced to come in closer to their opponents in order to reach them with their axes, war knives or swords, and the fighting will become more frantic and urgent. Eventually, those at the rear of one side or the other would decide that their side was losing or become too afraid of the fight and begin to slip away. At first it would be a trickle, just one or two individuals, then larger groups would begin to notice this and leave until the whole line was breaking and running. Alternatively, one of the pushes by a section of the line might break the enemy shield wall to much the same result. Either way, this is the section of battle where most of the killing is done, as the side running away will mostly abandon shields and weapons and be unable to defend themselves in their fear and panic. The other side, excited into a killing frenzy by the flight of their opponents, will chase them as far as possible - unless disciplined enough and ordered not to - killing as they go. Throughout the battle, a portion of the wounded will be slipping back through the lines, mostly during the natural breaks in the rhythm of the battle as both sides retreat for a breather, or might be pulled back to safety by a comrade behind them who shoves their way forward to save a friend. Not all will be able to do this, though, and will likely fall to the ground from blood loss and be killed as a result of their weakened state. Probably they will be trampled underfoot and become a trip hazard for both sides, unless one or the other attempts to use a break in the combat to clear the field of their dead and dying.

The short answer is that wearing armor in the heat is as uncomfortable as you might imagine, but it's better than being mortally wounded or dead.

The picture you might have in your head of a knight in full plate traversing the countryside until they encounter the enemy is fantasy, just as much as the image of fighters engaged in combat for hours on end. Armies would have any number of non-combatants ready to support troops as they rotate from some minutes of fighting on the front line, ready to help with equipment and refreshments.

Unfortunately, primary sources tend to not include minute-by-minute accounts of battles, only broad strokes and notable happenings. As far as my research has taken me, no firsthand accounts exist that directly answer your question, so we're left to fill in the blanks based on what we do have for historical accounts, plus the anecdotes of modern reenactors.