I'm kind of leaning toward the "stuck in recirculate mode" theory. The reason I don't think it is the heater core is that turning the setting to "defrost" clears the windows. If it were a heater core leak, the problem would exist at any setting, and probably get worse in defrost (at leat in the begining).

The manual says that the system is not in recirculate mode when in the defrost position, and the windows clear when in the defrost position. So, if it were incorrectly in recirculate mode in the AUTO position, the automatic defrost cycle would not work right. BUT, that would be an electronic problem, not a mechanical problem.