When using my cooler (round, orange) I preheat a bit with some hot tap water and then add the strike water, then the grain. Like Denny I stir until the temp stabilizes. After that I'll stir about every 15 minutes and add hot water if I lose temp from said stirring. Stirring seems to help the efficiency a bit as well.
When using my direct-fired stainless tun with RIMS, I also stir until the temp is stable and then let the RIMS system keep it there, but still give a full stir about every 15 minutes.