Today I had to adjust the mash bed with cool water since the strike was a little hotter than usual (mash bed at t=0 was 160 F). A while ago I had some issues with the standard lab thermometers (3 thermometers were giving me vastly different readings) so I bought a digital thermometer probe. The probe is nice since I can monitor different depths of the mash bed. However, today I noticed that I was getting readings between 160 and 140 F depending on the bed. I stirred the bed on multiple occasions (more than I would like), sealed the tun and waited. I figured that the bed would adjust to a semi-uniform temperature. 45 mins in right now and it hasnt. The variability improved somewhat (143-156). I had never noticed this before, but might have been because I used lab thermometers which cant be buried to different depths while giving a reading.
So my question is, is there is inherent variability in the mash bed (other specifics: rubber maid cooler, 30 lbs of malt), or is this an effect of fiddling with the strike water. If there is the inherent problem with differences in the mash bed temp, do you measure temp from a specific location or depth (e.g. middle of the tun, 4" deep) or do you look for an average temp across your measurements to fall into the 150-155 range? I would imagine that the size (lbs of malt) and shape of the container matter too.