I've got a rectangular cooler, so I've always just set the probe in the mash and closed the lid. But as TexLaw says, you don't really lose a lot of heat, so it's not really all that critical, it seems, to keep check of the temp.
Yesterday, in fact, I didn't use my probe thermometer, it's messed up and I haven't been able to futz with it to get it working. But, I have a digital pen thermometer that I like a lot and that seems to work great. I used that to confirm I hit my temps, then closed the lid and walk away for an hour.
When I opened it up, I found not that I had necessarily lost any total heat, but that there were a lot of hot and cool spots. One corner was still at the 155° I had originally set, while other spots were right about 150°. Now, I stirred well before closing the lid, but I'm not sure whether I needed to stir MORE or whether I lost heat from the cooler unevenly. I also never stirred the mash once I had the temperature set, figuring it was better to have uneven temp than to lose some heat when I opened it back up.
Lesson being - there can be a material difference in mash temp depending on where you are taking your measurement (and my hottest spot happened to be near a corner, not what I would have expected).