I would try a different tool here to isolate what the sensors and fan are doing. Download from the App Store Temperature Gauge (there are other similar temp & fan monitoring apps).
While AHT is giving you a heat error it is not able to tell you what the failure is because it can't in this case. It does not see a defect, only a condition (high heat).
More likely your system needs a good cleaning, dust and debris is likely clogging the fans ability to cool the system, the heat sink fins are clogged, and the logic board is coated with dust.
You'll need a ESD mat & wrist strap, a soft painters brush a can of can'ed air plus, the needed tools to open your system up. Carefully scrub the case and logic board with the brush, then blow some air to push the dust out. Repeat this on the heat sink fins and fan. just be careful in blowing the fan blades you don't want to blow them to hard.
Put your system back together and see how its doing using the monitoring app. Is it better or does it still having problems.
Let us know what you discover before and after the cleaning. Good Luck!