2005 crown vic climate control module bad blows through defroster only

I can't say 100% on this but some vehicles still use vacuum to operate the blend air doors (electric solenoids or earlier cable to operate the tempature door).
You may have a vacuum issue and defrost would be the default position because you need your winshield clear more than heat on your face or feet.
Start at the intake manifold and follow your vacuum source.

Had same problem with a 2010 Marquis. Vacuum tubes on engine firewall looked ok. Sent the EATC module to ModuleMaster in Idaho. Rebuilt it for 80 bucks. Works like new. I recommend this BEFORE having a professional tear apart your dash(big labor costs), or replace the module(800 bucks). Even if it turns out to be something other than the module, 80 bucks for a rebuild and warranty is worth it. And it just might fix it.