I don't believe that this is a viable option as the LM35 has a minimum operating temperature of -40C. What happens if the temperature drops below -40? Does it continue to read -40, or does it create an error message somehow?
Well, it'd help to know what the operating temperature range is. My assumption is that if they're reading the heatsink fan RPM, as driven from a motherboard header based on what the BIOS thinks the CPU temp is, then -40C isn't going to be an issue. I also assume attaching the sensor to the heatsink as close to the CPU as possible. But I admit those are assumptions. ETA:
Actually, going by the OP:
... that is currently controlling the fan mounted to the CPU heat sink.
That implies air inside the computer case. Unless he's (she?) using something like a very dry inert gas (which I think would be a poor thermal transfer medium). But let's talk about air. Cooling the interior of the case with LN2
is going to result in condensation and then frost on the motherboard and components. Maybe that's not an issue.
Again, more info needed. (See also Computer Cooling: Liquid Nitrogen