inconsistent heat

[LightlyToasted]

2007 4.8i.

Symptom: air through vents alternately blows warm then cool in roughly 30 second intervals.

Test: Crank up the temperature to max, choose auto mode, and go for a drive. Cabin never really gets up to required temperature. When it decides to blow warm the blower speed will increase, then 30s later it will decrease and the air is immediately cooler. The warm/cool cycle will repeat. Both driver and passenger sides are either warm or cool at the same time.

Coolant level is OK, coolant temperature gets up to 102C and holds steady so thermostat seems OK. Electric fan was replaced 2 years ago and operates normally.

No IHKA or any other relevant fault codes.

Auxiliary water pump was replaced last year, and appears to be operating OK when driving and during rest mode.

Heater control valve was replaced 2 years ago. IR thermometer shows input and output hoses are around 76C but it's hard to get a precise reading as they're crammed in the engine bay.

Any ideas? Perhaps a faulty interior temperature sensor is causing the mixer flap to go back and forth? If so, is there any way to test it via ISTA?