Thunderbirds had a rare problem like this. The blend door was not working properly. It would either stick or was not moving in porportion to the controls. There's a slim possibility you may have a similar problem. Since a computer has control over the door position, there is a position sensor on the mechanism to tell the computer where the door is. I don't know about this particular system, but the Tbirds used vacuum servos on the blend door. Low vacuum or a tight mechanism or a not properly calibrated sensor would cause a problem similar to this as the door would not properly proportion the amount of heated air versus not heated air. Granted, this is stretching it a bit, but it is a possibility. I just tipped 5400 miles on my LT3 and my climate control is ok. I've had no problems on the auto setting either. Even on manual it seems to maintain a good setting.
Speed costs money. How fast can you afford?