a layer of the paste??? It should be a very thin layer or it inhibits efficient heat transfer.
Where is the fan plugged in??? Is it plugged into a three pin connector on the mobo? That connection is controlled by a chip on the mobo that senses temp in itself and modulates the 12 volts to the fan in a on'off cycle of varying duty cycle. Possibly the chip has failed in the always ON mode.
Last year I installed a SuperCool CPU fan (it looks like a an exhaust manifold from a V
to correct a situation where the CPU cooler fan ran in high speed all the time. After replacing the fan it never came on high speed. Now it is doing it again. I took the fan apart cleaned all the dust, cleaned the unit, same thing. What is it the regulates the fan speed ? is there a thermostat ? oh yeah I made sure there was a nice even layer of that ceramic paste on the contact surfaces. Thanks for any ideas.

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