Heater blows hot air for a couple of minutes but then cold air after that

What is your question?

I turn on the car and the heater comes on. The fan blows. Warm air comes out for just a couple of minutes. Then, the air temperature switches to cold air blowing out. It fogs the windows.

What makes this problem better or worse?

Nothing

How long has your 2009 Honda Odyssey had this problem?

A couple of days