I was going to say Heater Core as well...my fathers 95 Dodge RAM had this same issue and you always knew it had to be the heater core.
2007 Smokestone LX HPP
'05 PI Airbox/Ziptube, BOC 91 Octane Tune, PowerSlot F&R Rotors, Raybestos Police Patrol Pads F&R, 260A Mechman Alt w/OAD & Big 3, Ported Intake Plenum, Adco Front & Rear Swaybars, Metco Control Arms, Metco Watts Link, PI Shocks F&R, Arnott HPP-spec "Limo" rear bags, Walker Quietflow 3's w/Resonator delete, 3.55 TracLoc conversion, 180 T-Stat, 22C Plugs, Pirelli P7 AS+ Tires, Kenwood DNX8120 Nav Headunit & Speakers, Viper 5901 Alarm/Remote Start
1999 PI, Former San Antonio PD Unit #171 (sold)
1999 LX (wrecked by a drunk while parked)
1987 LTD LX (wrecked by a friend who borrowed)