Regens involve injecting fuel into the exhuast to raise the temperature of the exhaust hot enough to burn off particular matter in your DPF. As such, it does effect the engine coolant temperature. The fans come on after you shut off the engine to dissipate heat in the engine bay.
If your temperature is fluctuating and your engine cooling fans are on after you arrive home you may have an engine cooling problem. Is your coolant level full? lots of particulate in the reservoir? are you losing coolant? where? is your car due for a water pump change - how many miles on it?
Regens don't happen all that often - maybe every 500-1000 miles or once a month in my experience. My coolant temperature has never exceeded 190 degrees (the middle mark on the guage) under any circumstance after 34,500 miles, regen or not, climbing over mountains, etc. Never.
To be certain as to why your engine cooling fans are on, get an app like EngineLink for your phone with bluetooth connection to OBDII port and check your exhaust temperature when the fans are on and check the engine coolant temperature too. If your gauge reads hotter than 190 I am thinking you have an overheating problem.
