Monitoring Mash Temps in Brutus 20, Recirculating System?

Hello, I am acquiring parts for a two vessel, 240 volt Brutus 20 system. While drinking up the last of the christmas ale on New Year's eve, my partner (the electrician) and I were debating how (or if) to monitor the temp of the mash in our cooler mash tun.

So two questions. One, is it worth monitoring the temperature in the tun, or do we just monitor the temperature in the kettle?

Second, and more complicated, where do you measure the mash temperature? From what I have read, it appears that a number of people monitor the temperature with a probe tee'd on the output valve of the tun. I am not sure how that works, however, since it seems the temperature of the wort exiting the grain bed would be different (higher) than the wort in the tun. Also, I don't see why that temperature is going to be any different than the temperature in the boil kettle, assuming you are monitoring temps during recirculation?

My feeling is I am over-complicating this (there was quite a lot of christmas ale involved) or I just don't understand the theory of a recirculating system.

Any help?

I have a RIMS system and I measure my temp at the exit of the RIMS tube right before it re-circulates back into the mash. I have only tried it this way, but I only have a .5 degree differential.

I'd think measuring it in the kettle is as good as anything. You're recirculating, it should all even out.