Referring here. 3" of 22AWG Nichrome, requires approx 0.5 amps to increase its temperature by 20C (68F). The resistance through the wire is ~0.025R, and increase in R due to heating up to 20C very small - assuming zero.E = IRE = 0.5 * 0.25 = 0.125v, is the voltage required to provide 0.5amps to a wire with a resistance of 0.025R and heat it 20C (68F) from 0C (32F). In which case given the very small R values in question, raising the temperature of the wire by 20C from any other temperature state, will require the same current and voltage.
Intuitively, this seems like too little power.
If your heater resistance is really as low as 0.025R you will have trouble with a MOSFET as they usually have an on-resistance of about 0.1R. Therefore most of your heating energy will be going to heat up the MOSFET.