If ever there was a more important time to brush your dog it is now in this heat! Clipping them short may not scientifically keep your dog cool, but it does prevent matting particularly with woolly coats.
A dog with matting around their neck is the same as you wearing a scarf as the air cannot get through the matted coat. Can you imagine, in this heat! Even very slight matting is restricting the air to get to the skin and the coat will contribute to the dog feeling hot.
Please check your dog, how easily can you run a comb through their coat?