I think an ESC will be unnecessarily complex for your application. I would suggest a simple motor driver capable of handling 2.5A (in practice...not just on paper). You can then control the heat by using PWM directly from the Arduino (use the analogWrite function).
Our
Rugged Motor Driver will handle the job if you put both outputs in parallel. There are lots and lots of other "simple" step/direction motor drivers to choose from.
PWM doesn't actually control the volts, it controls the *average* current through the load (your heated wire) hence the average power, hence the heat.
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The
Quick Shield: breakout all 28 pins to quick-connect terminals