A true indicator of the problems of heat and armour would be the solutions the crusaders utilized whilst on campaign.
Some sources state that the Saracens used a form of surcoat that covered the armour, a reasonably loose garment, of light coloured material which helped to reflect some of the sun's heat. This would also help trap an insulating layer of cooler air between the surcoat and armour. This was soon adopted by the crusaders, whom introduced it to Europe after the 1st crusade.
Helmets also evolved the visor, which could be raised quickly to survey the battle ......release heat.....or to improve breathing and quickly 'dropped' again. This was a necessary but dangerous practice.....skilled archers were always looking for raised visors so that they could target the face
Regards David