How can I determine the resistance needed to heat a wire to a specific temperature?
To regulate the heated wire temperature to 302&deg;F you should really plan to power the heating excitation circuit with a PWM drive that can vary the duty cycle over a good range. Use some empirical tests to at 100% duty cycle ON that the wire temperature can exceeed the 302&deg;F so that you have adequate control range to warm up the wire.

Next fix up your system to have a temperature sensing mechansism to allow detecting the temperature of the heating wire. One effective way to do this is to design you heater wire with an adjacent sensor wire. Bias this wire with a constant current source and then measure the voltage drop across this wire to ascertain the heater temperature. Use this temperature measurement to adjust the PWM drive to the heater wire in an appropriate manner.

The feedback of the sense wire to the PWM drive could follow a P (proportional) algorithm, a PI (proportional / integral) algorithm or a full PID (proportional / integral  differential) algorithm. The slow response time of thermal feedback systems often means that the simplest P only algorithm is just fine to maintain temperature control.