Since the concept of 32 thousand nukes exploding in a war sounded realistic (a bit on the "too many" side, but nothing completely impossible), I got into wikipedia to check if that was any particularly large bomb. I have bad news for you:
> The fusion-fission blast had a yield equivalent to 104 kilotons of TNT (435 terajoules)
That is a quite small fusion-fission bomb. If your calculation is right, we are talking about some hundreds of more normal ones, not tens of thousands.