One of the problems with hot-wire cutting is that the wire expands with temperature and a tensioning system is required. You could use this to your advantage and control wire temperature by controlling wire length. This in turn could allow very simple control from your AC transformer through a 'phase-angle firing module'. These are glorified dimmer controllers with a DC control input.

^{simulate this circuit – Schematic created using CircuitLab}

Your challenge with this approach is to come up with the linear transducer and some means of calibration. Setup would be by trial and error.

One of the problems with hot-wire cutting is that the wire expands with temperature and a tensioning system is required. You could use this to your advantage and control wire temperature by controlling wire length. This in turn could allow very simple control from your AC transformer through a 'phase-angle firing module'. These are glorified dimmer controllers with a DC control input.

^{simulate this circuit – Schematic created using CircuitLab}

Your challenge with this approach is to come up with the linear transducer and some means of calibration. Setup would be by trial and error.

For my one attempt at this I used a guitar string, E, 1st, 0.010". I had a 12 V, 5 A power supply and adjusted a contact along the wire until I got the required result.