Lagering, would this work?

Okay, I'm reading about building a "cold box" or using a fridge/freezer for lagering, but I'm short on time and for the next month or so, really short on cash. Here's what I do have. One huge commercial grade stainless fridge in an unheated workshop, with a Johnson temp controller.
Problem: this time of year that building usually maintains a temp well below 40°F where I want to lager my altbier for the next couple weeks.
Would it be possible to set a heating pad in the fridge (not under the carboy) and set the controller at 40° and lager away? It seems silly to use energy to heat something up only to cool it again, but that's the only immediate/cheap-short-term solution I've come up with.
Will this work? Anyone tried before?

I have a similar setup her in Calgary. I have a Ranco temp controller wired for heating my fridge in the winter (or for cooling in the summer). To prevent the fridge from freezing, I have an infrared heating bulb (bought at a pet store) inside that is controlled by the Ranco unit. Works perfectly, even when it is -20 outside.