I put a new heater core in my jeep last winter and had hot heat. Both hoses are hot coming out of the core, and the blend door seems to be closed all the way. I'm not sure what I'm missing??
If you have a hot hose going into the core and a hot hose coming out, it sounds like you have heat that's being blocked by something. Maybe the blend door should be open all the way?
I had to pull out a mouse house out of my Nissan Pickup every time cold weather started. I had put hardware cloth over the intake but they still got in. So if you have good heat going in and out of the core I'd look for a similar problem.