In a one meter diameter tunnel, or in this case, a long and really hot oven. 120MW are enough to turn a metric ton of most rock into magma every ten seconds.
In any case I guess Earthgrid will join the small club of companies and government programs who require extremely high temperature electronics. I'd also bet that these things will have limited sensors and give little feedback about what's actually happening in that tunnel. That or they'll need some fancy cooling idea or a pause until the tunnel cools down. Maybe the hot rock that is removed could be used to carry the heat away?
And that's just worrying about what the heat will do to your device. You'll also have to think about what it will do to the material you're tunneling through. Will the rock around you lose stability at higher temperature? Will water within the rock expand violently and collapse your tunnel? Will your device get stuck when everything around it turns into sticky goo? Will you set fire to whatever is close to your tunnel?
Finally, how do we actually get that much power? Certainly you cannot expect the local grid to supply that much. Maybe they could design and power it with a portable nuclear reactor? That's the same order of magnitude as a small one. Can't wait for the portable river technology that will make cooling all this possible.
I guess they could bring some 2,000KW diesel generators. They'll just need sixty of them. At around twenty four metric tons per unit and a combined consumption of 30,000 liters of diesel per hour that is going to be some interesting logistics.