When the t-stat opens, you should feel the flow through the main hoses from the rad. You should also see movement in the expansion tank as well. Your heater core could be clogged as you said.
Things to check:
t-stat operation. Pressure cap on expansion tank.
When heater is on full, does it blow hot?
Coolant level and mixture of 50-50 coolant/dis-stilled water.
