The heating effect of electric current depends on:
Material of a conductor
Quantity of current
Number of free electrons in a conductor
The heating effect depends on the conducting material as it varies material to material. Silver is a good conducting material compared to copper. Apart from this, if more and more current is passed through a conductor, it becomes hot in less time. This heating takes place due to the flow of free electrons i.e. these free electrons play an important role in generating heat due to collision within a conductor. More free electrons means more possibility of collisions within themselves, so more heating.