I am familiar with thermal resistors as I have used them before
The first thing I did was to measure the resistance between the black and white wire using my DMM. I measured a resistance of 270 Ohms I wanted to check to see if the resistor was still working, e.g. using a heat source you should see the resistance increase or decrease at a linear rate. When I applied a heat source the resistance increased but it would jump to random values.
I thought it was broken so I wondered if I should open the case to see if the wires were connected inside but as I ran my fingers along the wire I noticed the resistance returned to 270 OHMS then I knew it was a wiring problem .
To verify I cut the wires close to the sensor and tested the removed wires. As suspected the black wire was the trouble.
Using thermal wire I re-soldered a new wire to the sensor and then reattached the sensor to the heat sink
I also tested all the mosfets on the heat sink using my DMM. By measuring one's continuity and seeing if they all matched.
They all check out ok.
When the system is powered you will hear a loud click that is the relay switches so if your system does not turn on try replacing them.
When you open the top plate you will see a large heat sink, connected to the heat sink is the thermal resistor sensor.
You will need to remove the heat sink by unscrewing 3 screws on the bottom (left)
Also remove two side PCBs each have 1 screw and may have some zip lock cables that you need to cut(right)
With the top off now remove the ribbon cable by
1. pulling cable from slot
2. removing the one screw
3. cutting the black tape
4. With the cable off now un connect all the connectors from the PCB
Removed heat sink with PCB
If you examine the PCB part of the heat sink you will see two holes
1. The Blue arrow is the hole for the sensor to go into
2. The Red arrow shows the hole for connecting the sensors head to the heat sink using a screw.
Put the sensor in between the heat sink and PCB you may find tweezers are helpful to get it up through the hole
Then use a screw driver a screw to screw the sensor onto the heat sink .
Reassemble all parts and test to see if it works.
I was not able to find the schematic for this model but I found another service manual here
https://www.manualslib.com/manual/414315/Pioneer-Vsx-108-Av-Receiver.html
If you know of a link for the real schematic please past it on the comments below thanks,