How to regulate voltage of transformer output for nichrome wire
The simplest approach, given your setup, might be to substitute the dimmer with a relatively small (your primary current is &lt;1A) opto-triac or zero-crossing optoisolator, and regulate it via some form of rough PWM or analog control.

You can go all the way with a microcontroller/Arduino that measures the temperature of the wire (either by contact or with an IR sensor) and uses a PID controller to drive the Triac with a slow PWM waveform.

Or you can keep it simple and measure the current through the wire with a series resistor and capacitor that drives a simple transistor current-measuring circuit to turn-off the Triac photodiode. Something like this:







simulate this circuit &ndash; Schematic created using CircuitLab

You can also substitute D2 for an SCR and avoid dealing with the mains side completely. In that case the gate of the SCR can be directly driven like D1.

The only issue you have to be careful of, is that any regulation circuitry will be acting on average values of a non-sinusoidal waveform, so power calculations can introduce problematic non-linearities.