I have a 95 Honda Accord that I drive in the winter time and the heat is not working on it.

I felt both hoses from the heater core and they both feel warm. The thermostat appears to be functioning. My coolant level is good and I made sure there was no air in the system.

The air getting blown in the car is warmer than the outside air but I wouldn't say that its warm air...just warmer then outside.

Where should I begin to troubleshoot?

 

thermostat may not be opening all the way

 

You've checked all the basics already. I'm not sure how Hondas control the hot/cold door on the HVAC box, but it's either cable, vacuum, or electric motor. Since both heater hoses are hot, that's where I would check. See if the door is jammed or not being actuated properly.

 

If its not a blend door issue theres a possibility that there could be an animals nest in your heater box... Not totally uncommon, I think my roomates Ford Taurus has the same problem. Its warmer than ambient, but not by much. I'd pry open the case gently with a good flashlight and see if there is anything build up in front of the core (sorry, I'm not a big Honda guy).