heat works when I accelerate

I have a 2001 Grabd Am GT. This winter it started to have this problem when it would blow up hot air only when I accelerate, on iddling is blowing cold air( not as cold as it is outside but close).
Anyone has an ideea of what could be the problem?

Thanks guys.

Could be your water pump is going bad or you have a blockage in your cooling system.
As the pump fins rust off it take more rpms to move the coolant. A bad thermostat can do this too.

I would check the water pump first.
Then do a cooling system flush if one hasnt been done in the last 3 or more years and replace the thermostat.