This is very possible, depending on the style of your fridge/freezer. With the fridge/freezer I converted into an incubator this could have been easily accomplished. With mine, the freezer section is vented into the fridge section to cool the section. The use of a little great stuff expanding foam would have easily plugged the hole and allowed me to do what you are wanting to do. I converted the freezer to an incubator already and when I need the space for more clutches, I will convert the fridge section as well. I started with the freezer due to it being more insulated.
Hope this helps,
John