Are you implying that our furred ancestor didn't have effective cooling ability? ... that doesn't make sense ... all warm-blooded animal have internal temperature regulation ... including primates ...
Run an average man at speed for 30 minutes in high heat ... see what happens ... the marathon at the Athens Olympics is a good example of how the highest trained athletes fair under such conditions ... it was done but it weren't pretty ...
'Tis said ... that humanoids first stood upright, and then developed large brains ... it not that chimps don't make tools, just that chimps can't carry these tools with him, whatever he crafts must be left behind when the troope moves on to new feeding grounds ... he might find this tool again when the troope returns to this area, but generally speaking, for chimps to have tools, they must be constantly making them ... and not improving them ...
Human can carry tools, they only need two paws for locomotion, that leaves two paws to carry tools and food and babies and weapons ... instead of making new tools, humans can be improving the tools they carried with themselves ... now is when we develop the larger brain ... when better ideas meant better reproduction opportunities ... you know, before beer ...