That ribbon cable goes to this board with no obvious sh!tsta!ns on there …The MOSFETs will be at the other end of the grey ribbon cable that plugs in adjacent to the UC3708, follow that and see where it goes. It might go to another board or it might go direct to MOSFETs sat on a heatsink somewhere. If it does go to the board attached to the heatsink then yes really you should pop some new thermo paste on there for reassembly. Have you got / can you get a decent pic of the heatsink board?
The other board on the other side is also attached to the main heatsink but this is all you can see of that without taking it off the heatsink. Which I am reticent to do at the moment …
Bolts that seem to be attached to the heatsink visible here…