Well June July isn’t the peak Hot season but you are right to worry about temperatures that easily pass 110 F.
The Monsoon is a problem if you are travelling mid to south so to avoid those the further north you go the better.
I would have suggested Rajastan but that might be bad cause of the heat, so Kashmir is a good option (there are political and military issues but that’s more at the border shared by India and Pakistan) still worth seeing I’m told.
hope this helps