I'd say the old fridge should work fine - I've seen crazier grow cabs before. As discussed above, just be sure to have proper ventilation; I would position the fan as btfinn described - at the top, to push the hot air out as the purpose of the fan is to eliminate heat. You can have a secondary fan in the fridge to blow on your plants providing better air flow and strengthening their stems.

Also, what color is the interior of your fridge? Mine is already a pretty highly reflective white, which based upon my knowledge of fridges - most others are also. If yours is white, I doubt you need to go to the trouble of lining it with mylar.

Glad to follow this innovative grow.