To make the 880 into a milling machiene I would be inclined to get the squish down too about .030, this will help prevent preignition and heating of the exhaust side of the piston crown. Get an older 088 non rev limited coil so the saw AF mixture can be set with less guessing, open the muffler up and richen the jets. The extra HP gained by the saw not fighting the muffler restriction will allow it to work a little less to get the same work done. Same goes for some basic port clean up work. Keeping the RPM up with a little extra HP lets the fan do more cooling. Bogging the saw on a mill is real tough on it, produces a lot of heat but it slows the fan reducing cooling and then with the saw falling out of the powerband the cut takes longer (tripple whammy).
Good fuel and oil always, don't let the saw run dry in the cut. Keep the fan and cooling fins clear, let the saw warm up and cool down a little before and after big cuts and chain sharp.
All this is one reason why I installed a temp gauge. As you say, pushing the saw hard so it drops of the power curve and sits at say 6500 - 7000 rpm sees the temp rise noticeably. This is why I was slightly concerned with using an 8 pin with mildly aggressive rakers but it only dropped the operating RPM in hardwood by a couple of hundred rpm
My sensor is not ideally located (it's in a small gap above the exhaust manifold) so what the sensor measures is the temperature of the cooling air after it has passed over part of the cylinder. But it is still better than nothing.
As reported by the sensor, if the ambient air temp is 70F the saw at idle eventually reaches about 140F.
Milling sees it increase quickly but only by about 20F, then the temp rise slows down and the final operating temp depends on 101 variables. eg
How hard the saw is being pushed
Wood hardness
Amount of contact between wood and saw or width of cut
Sprocket size
Size of chain
Sharpness of chain
Depth of rakers
It's easy to see the effect or some of these factors eg the temp increases quicker if the saw is pushed hard and dropping the RPM, but I can't really see any temp difference between using 7 or 8 pin sprockets.
As I said, once the saw has reached a nominal operating temp ~160F, the temp continues to increase. All being well, the final temp at the end of the slab (~170F) is a useful indicator of how things are going. If I don't touch up the chain and cut another slab the temperature at the end of that slab can be 190F.
When ever the saw has been working (eg sensor measuring ~170F, ) and then left to idle (or stopped) the temp at the sensor rises immediately by about 30F at idle (and over 50F if stopped) because the amount of cooling has dropped off or ceased.
I then leave the saw to idle until it reaches <150F - this can take as much as 2 minutes.