If you cut off the sensor that causes minimal RPM. At that point you would want to power it directly from the 12V rail, it would run slow, probably too slow, possibly even failing to run at all until the system temp was too high.
If you instead want to have control, consider how the control circuit works, what it's limitations are. Bridging, soldering, etc, the thermal sensor leads causes max RPM when the fan control circuit tries to cause max RPM, but if a fan is especially high RPM without any control it may be too much noise, wear, or dust buildup for your needs. Therefore, unless you hand-pick an optimal fan (max speed per model), the ideal to reuse one you have is to put a resistor in parallel with the existing thermal sensor. Generally, the value of resistor needed is inbetween 1K and 10K, but that's just what is common, it's not a rule or anything. The thermal sensor feedback is a low current circuit, instead of a fixed resistor value you could make it adjustable by using a 20K POT instead, though depending on the thermal sensor used it might be more precise with a lower value POT.
In other words, the best course of action is to measure the thermal sensor resistance value at typical system heat levels (or open air will be close enough) and pick a POT that is about twice the value of the thermal sensor reading.
On the other hand you could just say screw it and run the fan at an RPM a little higher than what the system needs at it's lowest processing/heat levels, and accept it will get a few degrees warmer under load, so long as it doesn't get hot enough to be instable or effect lifespan beyond what you deem acceptable. The latter is what OEMs usually [Edit:] did, before they switched to single rear fans for CPU heatsink and exhaust controlled by the motherboard thermal sensor fan control circuit [/Edit], and manage to do so while being fairly quiet, but they have less cooling subsystem redundancy, less ability to o'c as far, upgrade as much, and they don't care what happens after the warranty ends.