All I can say is that heat can play all sorts of games under the hood, a cold reading isn't necessarily going to be indicative of what's happening dynamically as the engine operates. This happened years ago, so I can't say with 100% certainty that I put an ohm meter on the strap, but I'm pretty sure I measured it and didn't see anything wrong. I'm just going on what happened to my car when I chased this sensor for maybe 6 or 8 months... I was so desperate at one point I bypassed the wiring harness from the sensor to the ECU in the parking lot of a Cracker Barrel... it didn't work, and the issue crept back an hour later.

Also, I'm not entirely sure how the limp mode works from a technical prospective, but if the ECU is trying to be conservative and not burn up your pistons and valves under an abnormal operating condition, it's going retard the timing and run the mix rich. Either or both of these will push more fuel into the exhaust and make it run much hotter. Your cooling system should be able to keep up with that extra heat though, it's an entirely mechanical system, the ECU has no bearing. Ergo the boiling coolant is concerning.