The regeneration cycle is designed to burn out the soot and particles captured in the DPF. To do this, the engine must get hot and then start the cycle, which burns more fuel to increase the exhaust gas temperatures. It makes reasonable sense to run the engine hard, preferably under a load, to get the engine as hot as possible to aid in burning out the stuck particles.
When I know the regeneration cycle is about to commence, in an hour or two, I will try to do something with the tractor: Go out and mow down the field, do some loader work, regrade the driveway, etc. Just to work the engine before (or perhaps during) a regeneration cycle. When I see that regeneration light come on, I typically firewall the hand throttle. This is not needed as the ECU will run up the engine to the required RPM on its own.
While more is not always better, in this case it is. More heat means more burning of the particles retained in the DPF. More heat is gained with the engine running at it's full potential under a load. While the ECU can rev the engine to the required RPM to achieve regeneration, running it faster and hotter is best. Just pay attention to the tractor during regen. Watch for overheating, runaways, etc.
If the tractor is overheating, during a regeneration cycle or under a heavy load, then there is likely a coolant problem. The most common cooling problems encounterd with these tractors is a clogged radiator. However, low coolant levels, loose belts, bad thermostats, and bad water pumps can all contribute to overheating. Make sure you keep the tractor engine clean as well. A thick layer of oil and dirt adhered to the engine block acts as an insulator. If you're experiencing overheating, do all that you can to keep it cool.