Because of the thermal mass in your mash tun, you really don't need to worry about temp fluccuations much. My PID kicks off at the exact moment it hits my set temp, but because of residual heat, the temp still reads higher for a few more degrees. It will kick back on as soon as I drop a degree below my set temp. Even though it may read 2 degrees high or low at any given time, the mash is always constant. It won't lose heat fast enough to make a difference.
Add in circulation, and you'll be fine. I monitor my temps through my PID, analog thermometers on my kettles, and a digital thermometer every 10-15 minutes. Other than my PID, everything reads exactly where it should be.