Did this on my '04 Hemi about a year ago. Fixed it no prob. It's a common problem to all Dodge pickups of those years. The recirculator door breaks and falls down, blocking the vent. It's a fix for the AC, but probably your problem. Easy to check and fix if it turns out it is the prob.
Don't get suckered into the $1,000 shop fix. Just yank the broken door out and be done with it.
The fix