Is heat an extensive or intensive property?
In thermodynamics, heat is not a function of state but a process function. So for the question


  Is heat a property of matter?


the answer is no.


  ... is it extensive or intensive?


Since the concept of intensive and extensive properties only applies to physical properties that are a function of state, heat is neither intensive nor extensive.

As Chester said in the comments, it is worth noting that heat (as well as work) applied to a system can cause changes in the thermodynamic equilibrium state of the system.