Is the issue that if losing air flow as previously suggested or is it that the temperature drops from warm to cold ? In later model jeeps there are issues of blend doors in the duct work that cause such problems as your experiencing but I'm also reminded of a friends wife's ford van which had a similar problem . Heat would be lost at idle and only improved when accelerating .
in the case of this ford can , it would up being a water pump impeller not moving the engine coolant so circulation was poor . Amazing there was no overheating . We replaced the water pump . Fixed it . The impeller blades were so worn that the ability to even move coolant through the water jackets was probably reduced to half , at best .
Not saying that the water pump should be replaced in your Jeep Liberty but the circulation should be checked in the radiator to confirm that it doesnt have a similar problem . It the circulation checks out and there is no issues of running over the normal temperature , it is likely there is the issue of the blend doors . That is within the duct work of the vent system inside the dash .
