Yep you can get those bandanas that freeze here in Australia... we had one for Kona but to be honest, it really didn't do much around her neck but putting it under the 'armpit' on her front legs really works well.
I find that Kilby handles the heat much better than Kona but I also take a water bottle with me on walks if it's warm. Actually, I take a back-pack with the water in it because trying to walk 2 boxers and carry 2L of water is pretty tiring for me! Both girls very happily drink out of the 'pop-top' bottles (it's like feeding baby lambs from a bottle.... so cute).
Dogs also cool themselves down through their feet... Kilby will often put her feet in water to cool down if she can. Note - the other dogs at obedience class were not so impressed by her trying to get all 4 legs into a standard size bucket (the group drinking bucket) at the same time... it was pretty funny though! So if the ground is hot, puppy's pads might be heating up too?
Anyway, it will be a while before you can take go on runs (best to wait until they are around 18mths+ as they still have soft joints/bones and you can risk injury) so just take it slowly (go earlier or later in the day if you can) and gradually build up fitness. Try going earlier or later in the day if you can.
But, I think you're doing the right things taking your cues from them
