Arduino logic level mosfet
I will need just about 100ma at nominal battery voltage to reach my
  desired temperature.


I'd consider using a low voltaget op-amp and a darlington transistor like this: -



With 1 volt in, the op-amp's negative feedback ensures that 1 volt appears across the 10 ohm sense resistor and this largely ensures that 100 mA flows through the nichrome wire in the collector.

You need to choose an op-amp that can work down to 2.8 volts without spitting and moaning and the Darlington is preferable over the MOSFET because of instabilities due to gate capacitance.