How can the leakage of mitochondrial protons generate heat?
Uncoupling ATP synthesis from the ETC (electron transfer chain; this is where oxidation takes place) by thermogenin or any other method means that the energy used to generate or uphold the proton gradient gets 'lost'.

Since physics teaches us that energy is only transferred and never truly lost, the energy consumed by the ETC must most go somewhere - heat / thermal energy is the easiest and therefore most likely option.

References


Wikipedia article on Uncoupling Proteins
Uncoupling article written in chemical terms
Short general article about brown fat and heat production