I have a 2002 Taurus SES. When I turn on the heat it blows warm air for about 30 seconds and then the air goes cool. If I turn the heat off for about 10 minutes it will blow warm air again for about 30 secs but goes cool again. I've replaced the thermostat but it did not fix the issue. Has anybody seen this before? Any suggestions?

 

Two things that can cause that problem could be a plugged heater core or possibly air trapped in the heater core itself.
If you can, the better way to flush out the heater core is to disconnect both hoses from the engine and run water from a garden hose thru the hoses and the core to flush out any sediment. Depending on how much you can dislodge will improve the flow of coolant thru it.
To confirm the problem, with the engine hot and running, heater on high speed for heat, both hoses coming off the heater should be and stay hot. If one is hot and the other is cool that would confirm that the core is restricted.