Weird. I can plug mine in while turned on. Well, start by checking the obvious, apologies if this is redundant. Mine is white wire in front, red middle, black in back. Check the plug carefully, make sure the leads are all fully seated. I just tried putting the plug in at angles, sure enough at least once, when I think I was connecting the white/front side first, I got the beeping and too low temp mess. I started to try and pull the wires from the connector to really figure it out, but couldn't seem to get them out. And I'm willing to help, but only to a point!

If the connectors all check out, perhaps the sensor itself is not right somehow. These chargers are sorta common, especially at a race track. Try that if you can, find another one and plug your sensor into it.

Do you have a multi-meter, or access to one? I checked resistance on my sensor. I'm getting around 1.7Mohm from white to each red and black. Between red and black I'm seeing 47kohm.

Good luck!