Ive been having somewhat of the same problem with my 06 2500 HD, how ever mine goes up to 250*. I've checked it with a heat gun & its only showing 186 max but gauge will be around the 250 range.
Most people said it was the interal harness.. Swapped it out with a OEM from GM & it doing the same thing. Check volts & ohms to & from everything & its still showing trams temp sensor is bad..
Haven't got around to replacing it again.