Correct. The control for the mix valve manual and automatic is through a common wire. So it is most likely a wiring/switch problem upstream of the valve c/p.
Regarding your question:
The B737-500 uses the mix valve. On the 737NG, I'm pretty sure the -600 uses the mix valve, and I know that anything larger than the -700 uses the Trim Air temp ctrl sys (Zones) and the different pack (condenser/reheater cycles). The condenser/reheater pack and trim air sys are bascially the same as the -400 as I understand.
You're a bit confused.
I'll explain as best I can
Some Basic B737-300/500 pack components:
Pack valve (Flow Control and Shutoff valve)
Mix valve: Valve has 2 sides, one hot and one cold. They are 180 degrees out of phase, meaning that when the hot side is open, the cold side is closed.
Air Cycle machine
Flighdeck selector panel: Includes temp selector switch. Manual mode manually positions the mix valve. In auto mode, a cabin temp controller uses sensed temperature and desired temperature to position the mix valve.
Hot bleed air flows thru the pack valve when the pack switch is turned on. When the pack is first turned on, the mix valve is in the full cold position, which means that all air will go thru the cooling cycle. This hot air from the cold side of the valve goes through the ram air cooled primary heat exchanger to remove some of the heat from the air. This air then goes to the compressor side of the Air Cycle machine to provide the initial drive (The turbine side will drive the ACM later). This compressed air, now hotter will leave the ACM and got thru the secondary heat exchanger. The Air is then cooled again. This air now goes to the turbine section of the ACM. The air is now expanded which is how you get the cool air.
The flightdeck selector panel for the temp control has a switch that has 2 modes: Auto and manual. I will just focus on manual now. When in manual mode, the switch is spring loaded to the center position which provides no signal to the mix valve. Position the switch to cold and hold it, and the valve will drive to the cold positoon (allowing the majority of bleed air to go to thru the cooling pack cycle). When you drive the valve to the hot side, you change the position of the valve. The cold side will start to close and the hot side will start to open. When the hot side starts to open, it will allow some of that bleed air to bypass the cooling cycle. This air outputs to mix with the output of the cooling pack (which is now a less because there is less air available to drive the ACM), thus the air is now a little warmer.
Alot of this stuff might be hard to visualize, but maybe you can. Hope it helps.