The thermostat sits on the bottom of the V:
8 hours labour is over the top. Yes the air box has to come out - a 10 second job as it just pulls out of rubber mounts! Do not let the garage over state the job.
However the fact that the cooling fan worked "after it was fiddled with" does not sound good, it needs to work promptly and reliably. You have to understand how it works:
The fan runs with either 2 or 3 speeds. When engine temp rises low speed will cut in which is usually enough. However fan also runs on low speed when the aircon is switched on, so after some years, low speed will wear out and fail first. That's why we are suggesting checking if it runs when operating the aircon - if not then there is a problem which must be fixed.
If low speed has failed then the engine will get hotter and hotter, until eventually high speed emergency will cut in, however by then it is on the threshold of danger. This can lead to the coolant boiling and overflowing, even with the fan running. This is why a faulty fan could be the root of your problems, and why it must be checked.
Understand also that the temperature gauge is next to useless - it is designed to remain still between 75 and 112oC, so when it does finally rise it is often too late. It may as well be painted onto the dial.
Carry out the check indicated by Stocktake above, and post the result. The V6 cooling system works perfectly well if all the components are in good condition, so once the fault is found and repaired you will have no more issues. Blind guesswork however will lead to disaster!
Alternatively, if the cooling fan is working correctly following your tests, then follow the advice given already and check for coolant in the engine V, a sure sign the plastic thermostat housing has split and is leaking.