Given some debates I've seen on this issue in the past, I'm amazed no one else has responded to this. You can see photos of my temp probe installation in my mash tun
here. Without my mash tun in front of me with ruler in hand, I'm guessing I installed that 3 to 4" above the false bottom. I wanted it closer to the bottom than the top since the hot water and recirculation starts at the top, and I might do batches with less grain some time. For a high gravity 10 gallon batch, the probe is about 1/4 from the bottom. For a middle gravity 5 gallon batch, it will probably be right in the middle.