If you have a 'remote thermometer' or thermal image machine you can test the inlet and outlet hoses on the heater core. They should be fairly easy to locate where they pass through the firewall, usually on the passenger side. Those hoses should heat up pretty quickly; and one should be significantly warmer than the other if the heat is running and making heat inside the vehicle. If you completely turn off the heat they should be close to the same temperature.
In the absence of any remote options you can very carefully test them by touch. Just use the back of your hand and do not 'grab' them.
They both should heat up pretty quickly assuming there is no thermostat issue. If they really never get near to hot enough then it may be a stuck open thermostat. If one is warm/hot and the other remains cold then it is likely a clogged core.
If all the above checks out and the inlet and outlet hoses are hot/warm then the issue is likely inside at the actuators/doors.
I have a digital thermometer with the long prong you use for meat or in my case soil temps. Wife drove the car for a few minutes and came back. I got 42.1 C or 108 F on the inlet hose (top) and 27.7 C or 82 F on the outlet (bottom). While she was driving the heat was on as the rear was blowing hot air, but the front was blowing cool air (in all settings).
I left it for a couple of hours and tried both hoses. They were at about 2.1 C (36 F) for inlet and 1.7 C (35 F) for outlet.
Also as I didn't confirm beforehand, I did open the rad cap when the car was cold and the cap was looking good and coolant inside was nice and green. And the temp guage looks normal. No sign of overheating.
As the blend door actuators aren't making any clicking sound like the it would with a broken gear, I'm not sure how else to check. I can see the driver's side one (haven't looked on passenger side yet). Perhaps unplug, unfasten from car then open it up to look to make sure no gears are cracked/broken and that they are turning fine? Or I guess maybe I don't have to unplug from the car but just unfasten it and take the cover off and see if the gears are moving while I change the direction settings of the heat?
It's not like it's stuck on hot OR cold. They both are blowing cold for at least 10 mintues before they blow hot air. And that's in all settings, including defrost. So the doors will move. So I'm kind of at a loss right now.
And based on the temps of the inlet/outlet hoses I mentioned above, sounds like the heater core is not clogged? And the thermostat is probably working fine? Is it possible a sensor is failing? No idea where that would be or how it works.
I'm starting to think I'm going to bring it into the shop. I do have to do the brakes on my Accord in the next few days. I'm thinking I can talk to the mechanic about that for a couple of minutes and see what he says.