Heat works but then stops after a minute

Alright, when my vehicle is at operating temperature and I turn on the heat it will blow heat then get cool after about a minute. Both heater core hoses under the hood are warm, lower is warmer than upper. I pulled out the blend door and got no change, the thermostat is in working order, cooling system is bled. I am out of ideas. If I keep turning the blower motor off after it gets cool and back on, it blows heat again and then gets cool again and so on.