It's an old expression, but when someone used it today it made me wonder about how the phrase came to mean what it does.
Coinage would not seem to bear an association to being on fire, though if metal coins were red-hot they certainly would sear a hole through most clothing materials.
Paper money can catch fire, and would then catch fire to clothing in order to burn a hole.
The pocket is general sewn of material that is a lighter-weight fabric than the rest of the garment, resulting in it being easier to wear and acquire holes (that can lose money and other valuables)
I understand that the word 'hot' has a general usage to mean 'moving fast' or otherwise 'very active'.
So, I grasp that this can be associated with the desire to spend money. I then can make the humorous-leap to said 'hot money' effecting a hole in one's pocket. I'd really rather hear an explicitly validated origin, rather than me making up all this in my head, though.
Best Answer
Money burns a hole in my pocket.
The Phrase Finder shows very old usages of the idiom, which clearly suggests a sense of urgency to get rid of something because it is supposedly too hot: