The fan control system(hardware) is malfunctioning, the fan is delayed

My MacBook becomes stuck and shuts down.

Even when the Mac is hot (57°C| 70°C| 85°C| 90°C), it becomes stuck or shuts down, and the fan activates with a delay; the fan then begins to run at a low speed; and the fan continues to run at a low speed.

If I set the user to auto login, it works with the MAC's Fan Control set to 4000RPM, because the Mac cools down and then works with Safari and other apps and tasks.

Mac's Fan Controler is acceptable, but it does not work properly with the auto option; however, it works well with custom rpm.

My Mac's fan controller is set to auto and/or 3000 / 4000 / full blast.

Concerning my MPB:

- MacBook Pro (13", 2017, Two puertos Thunderbolt 3)

- Intercore I5

- MacOS Catalina 10.15.7 The Apple Hadware diagnostic test has been passed: There was no problem found.

During the recovery boot and diagnostic hardware test, the Mac becomes hot (57°C| 70°C| 85°C| 90°C), the Mac becomes stuck or shuts down, and the fan activates with a delay.

Update:

After reading @danj answer, this is what I've done:

1- Clean the fan blades (I had already checked them and they are not obstructed or dusty)

2- Apply thermal paste to the CPU only on the chip, a thin layer (the thermal paste does not completely convince me since it has a thermal conductivity of 0.7W/MK, it is of the Sabo brand and it is composed of silicone and metallic oxide)

3-I bought the TG Pro license.

Despite all this, I cannot work with confidence since the moment the temperature exceeds the threshold of 70 -80 degrees Celsius for a fews seconds or one minute the Mac shuts down.

I rule out the idea that it is a MacOS problem since in the boot manager, I have left it for a few minutes and it turns off, I am only able to keep it on with the TG Pro application, with the Auto Boost option well configured (to the extreme).

The fan(s) turn off by the hardware if the temperatures are low enough, and takes a long time to turn on when the temperature starts to rise, I have taken extreme measures and completely disabled the system, and assigning the work to Auto Boost:

Here the configuration of TG Pro Auto Boost:

Sensor temperature recorded by TG Pro app:

I am testing CPU load with Endurance App:

By stressing a CPU core (2 or more cores, the collapse is extremely fast) I have managed to keep it on for at least 13 minutes, after which it can overheat and shut down, TG Pro does what it can to keep the Fan at full blast.

I have two hypotheses:

1- The heatsink is not being able to cool the CPU in time, either because of the quality of the thermal paste, or because the aluminum heatsink is damaged.

2- The hardware shutdown of the fan is taking too much control of the fan and is reacting late (but I discard this hypothesis because TG Pro is able to make the fan run based on the Auto Boost rules)

The TG Pro diagnostic indicates that everything is fine, as does the Apple Hardware Test.

Post Data: While I was writing this message, I had several safari tabs open, as well as vscode. Everything was fine until I installed Google Chrome. I hadn't even opened it - I just copied it to the applications folder. In the process of copying, my mac collapsed and turned off.

Update 07/01/2022:

Please note @danj

CoconutBatery - battery health:

@danj temperature with power adapter connected

@danj please see this update:

TG Pro capture:

coconutBattery capture:

Also, I noticed that the heatsink contact on the logic board is separated from the motherboard; please see the images in the pink-colored area:

I could feel a sudden temperature increase in an inductor R22 in the area of the CPU, which could be hotter than the CPU itself.

The yellow zone, but especially the red zone within the yellow zone.

To transfer hot temperatures to the Bottom Base Cover Panel, I installed a 12 W/MK thermal pad in the heatsink and the R22 inductor near the CPU as a precaution.