I use a similar one , with basically the process you described .
I strike , stir it all in good and drop my probe to about the center of my grain bed and close the lid. I use 1 lbs of rice hulls in every batch ( 5 gal.) to help to keep the temp. even in the grain bed. I believe I got that from reading Gordon Strong's Brewing Better Beer ( great book ) . This way I have a good idea of the temp throughout the mashing process . If it starts to drop I aggressively rock the cooler a time or two and often the temp will come back up a couple degrees.
It is interesting to watch the temp . At first I often see a drop then a rise to my target range. At about 40 min I loss a degree or so , but that temp will normally hold even out a 90 min mash.
Your not direct fire so remember your target temp is going to need to be a +\- range and you will likely drop a degree as time goes on . So if you wanted 150 don't stress over 151 or 149. Watch you system and learn how it reacts to changes. I have hot running water in my brewing area and have the heater set to a scorching 170f when I am prep-ing at the start of my brew day I fill my cooler with hot water and let it sit till just about mash time and then drain it through the ball valve . This gives the valve a good flush and preheats my cooler. I brew on a raised wooden porch so I am able to do lots of dump and drain stuff without a mess. Sorry , I may have wondered off topic , but these are a few things I thought might be useful to ponder.