Would a bad thermostat cause heater to not get warm? It only warms up when truck is moving. If I let truck sit and warm up it only blows cold air.

If it's stuck open maybe. But most likely you have a blend door motor/actuator issue.

www.youtube.com/watch?v=aA-OADF-_q8 -- check this out. It's for a 2008 but I think you are having a similar issue.

Opps I didn't fully read your question. With it warming up while driving it could be a faulty thermostat causing it. After it has sit idling for a while feel the hoses going to the heater core. Are both of them hot? Is only one hot? Is neither hot? This will help diagnose your issue.

OH didn't say it was a diesel in your question. Seen it in your other question Diesel's are horrible at making or maintaining engine heat at or near idle due to there effiicency. Options are a high idle setup. Winter front is a must should warm up a little faster once you start moving. Do you have a electric block heater, plug that in until you start driving. If you really need heat I've used diesel/electric heaters to pre-heat the coolant and to keep heating it when the engine cannot. They are not cheap but they are handy. Webasto, Pro-heat and Espar are the main brands. I ran the Espar in my stuff. They consist of a small water pump and a diesel (or gas) burner. The unit uses diesel from the trucks tank to fire the heater. The unit circulates your coolant (usually you tie into the cab heater hoses) from your engine through your heater core and back to the engine and will burn on high until about 60 deg C and then maintain the heat in low burn mode. With the dual batteries in your truck the Espar could run for 3+ days at .25 of a gallon of fuel an hour. The cool thing is that that also have timers so that you can preset when the unit is to start-up and how long it runs for.