65 mustang standard coupe with no A/C heater blowing cold air

Yes, do check the thermostat for correct operation and temperature range. The heater core could also be flushed and/or need to be replaced. The usual cause of this problem is that the foam pads and seals inside the heater need to be replaced due to aging. This is a fairly common problem. Kits of all of the parts are readily available from most Mustang parts suppliers. The heater assembly needs to be removed to do this and it should take about 1/2 day from start to finish.
Hope this helps and have an excellent day!
Ron

I had the same problem with my heater. Take out the heater core and start flushing it by putting a garden hose with a smaller spray nozzle into either hose tube thing.

Keep pumping water through one side until the water clears up a bit, then go to the next side and do the same. Keep going back and forth until you do each side at least ten times, or until the water comes out clear right off the bat.

65 mustang, your a spoiled brat ! ha-ha NICE !! If I remember correctly, the heater hoses,(which you can actually see & get to easily) don't have any valve in between engine & core connection, so start there at firewall area & feel the hoses when engine warmed up, they should be close to same temperature indicating proper flow.One hot, one quite a bit cooler tells you probably plugged in core. After that if all's good there, your heater controls are cable driven and you should be able to get to them under the dash to make sure all doors are moving as they should. Temperature gauge is in good operating range for heat when engine warmed up? (thermostat if not)

possible clogged heater core