[v8volvo]

^^ I believe that is correct, no particular orientation needed. Generally the orientation only matters if there is an air bleed hole in the thermostat (as post #7 above mentions). I don't think the D24/D24T tstats were ever meant to have a hole like this, since with the thermostat located down low in the block, and right at the inlet of the water pump, an airlock at that location is almost impossible anyway. The bleed hole matters more in engine designs where the tstat is located up at the top of the motor. None of the D24/T (or identical Audi spec) thermostats I have ever bought in either of the two prevalent temp ratings has had a bleed hole.

I think some of the greenbooks mention there being an arrow or a hole to worry about since maybe the earliest engines' thermostats did have one for some unnecessary reason (maybe just Volvo's habit since their own gas engines put the tstat up top), but they presumably eliminated that pretty soon once they realized it served no purpose in the D24/T engines other than slightly reducing the thermostat's overall effectiveness.

For our engines, air can be burped out of the cooling system using the greenbook's recommended procedure of disconnecting one end of the hose running from the head to top of the cold start device housing on the IP, as you're probably familiar with. That procedure works well.