Why is this circuit causing my breaker to trip?
The breaker is almost definitely tripping from an overcurrent.  

As to why it would only happen after a certain period of time, the resistance of your heater is liking decreasing with temperature. So you are actually drawing more current once the heater is warmed up.

If you dig deeper into the data sheet for the fuse you might find that it will not trip that quickly for 15A.  Check out the current versus time curves on the data sheet.