Why would it be hotter? The fridge would be warmer because all the cold air would be escaping out to the room, serving as an extremely inefficient air conditioning...
Extremely inefficient air conditioning would be if she'd put a tent up in front of it ala The Simpsons. This is just flat out wasting energy (in fact, the room outside of the area directly in front of the fridge, would be even hotter, because refrigerators only move heat, and they use energy to do so...)
Laws of Thermodynamics. Specifically the Second Law: "In a system, a process that occurs will tend to increase the total entropy of the universe."
Or in more applicable terms, as the Clausius statement: Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature.
Informally, "Heat doesn't flow from cold to hot (without work input)", which is true obviously from ordinary experience. For example in a refrigerator, heat flows from cold to hot, but only when aided by an external agent (i.e. the compressor). Note that from the mathematical definition of entropy, a process in which heat flows from cold to hot has decreasing entropy. This can happen in a non-isolated system if entropy is created elsewhere, such that the total entropy is constant or increasing, as required by the second law. For example, the electrical energy going into a refrigerator is converted to heat and goes out the back, representing a net increase in entropy.
In other words: To keep the inside cold, it makes the outside warm. Much warmer, in fact, than the chill inside.