The BE6-2 has a built in CPU temp monitor (and system temp monitor), unlike the original BE6 which had a built in system temp monitor but you had to monitor the CPU with the included thermocouple.
The thermocouple included with the BE6-II can be used to monitor the temperature of anything in your system...hard drives, video cards, etc.
If you want to double verify the temperature of the CPU using the thermocouple, then you need to tape it onto the CPU such that it touches the side of the core. The core is the little metallic piece that sticks up in the center of the CPU...which the heatsink rests on. Note that the thermocouple will measure heat at the point where the two wires first come into contact...which should be at the very tip if I remember what the one that ships with the BE6-2 looks like.
As long as your not blocking the heat transfer from the core to the heatsink, you're ok.
If you remove the heatsink, remember to reattach it using good silicon heatsink compound. Remove all traces of the old pad or dried out compound before applying new grease.
Your CPU should run between 40C and 65C in my experience. If you're at or over 70C then you might consider a better cooling mechanism. You can find actual CPU operating ranges on Intel's website. I think higher up PIII's will operate up to 80-90C, but it's of course recommended to cool them as much as possible (without going overboard).
Definately use that hardware doctor software than came with the mobo. It's ugly but a usable tool.
Slackmaster 2000