I did some milling with a 362 and a 32 inch bar. Don't push to hard and you will be fine. Let the saw idle for at least a minute before shutting it off. Let it cool off between cuts and i think you can get away with it.
When you start the saw after it is warm do not move the master control lever to choke-cold start. After the saw is warm it will start in one pull without moving any controls.
If you choke a M-Tronic when it is warm they like to flood and not restart until they are cold.
Do not use the start mode when the saw is warm. The start mode will flood the saw. When it is warm just pull. Do not touch any controls. It will start just fine.
I mill small beams with a ms362. No problems even on long cuts. I did a cut on a 16 foot beam and used a tank of fuel for the cut. I think that should be a long enough cut to melt it if it was going to melt down.