Ford F150 - bad heater core on my 91?

Just got the truck yesterday so I'm not too sure of the history. It no heat, but it blows. Hose on right is hot to touch, but hose on left is not when the engine is warm. Is this a sign of a bad core? Could it be anything else? I know cores are cheap in the lower 48 and can be had with a 30 min drive. However I must order off the web or pay a 150% markup at the small SNAPA we have here and wait 2 weeks for it to arrive. Thanks in advance.

First take off the hoses at the engine end and using a garden hose force water both ways through the core. You will likely be surprised at the crap that will come out. At this point flush and refill the cooling system and you should be good to go.

Cleat

Napa actually had a core in stock so put it in and flushed the system before hooking up the hoses. Took as long to flush as it did for the install.

Now on to fixing the pass door lock (see new post).