My heater cuts out in my 2001 Buick LeSabre... what could the problem be?

My heater cut out last night on my 2001 Buick LeSabre. I had been driving for about 1 hour. It was freezing, in the teens. I cut the heater off, waited a few minutes, cut the heater back on, and felt warmth, but as soon as I cut the fan on, it became cold.

Here is what I would do

1st. check to see if there is enough coolant in the radiator. You should also check what the antifreeze is rated for temperature wise.

2nd if that is good then you might consider a new thermostat.

3rd possible that your heater core is in need of a flush or replacement.