(Note: this is similar to is Cryomancy scientifically possible?, but not exactly the same.)
In my story, I have "magic" that amounts to telekinesis powered by the user's metabolism.
It seems that heating objects using this magic should be pretty plausible (although the amount of heat that can be generated is somewhat limited); the user metabolizes some energy, and that energy, instead of doing Work inside the user's body, causes a target object to heat up by that amount of energy. More specifically, the way I envision this working is something like the user's body produces energy via metabolism as normal ("using magic" can be though of as an additional way to trigger metabolic energy production), but the energy produced is magically teleported to a location of the user's choice and acts in a direction of the user's choice. (I think this is sufficient to blur the lines between "heat" energy and other, more useful forms of kinetic energy, thus explaining why a magic user can also do things like levitate small objects. This is playing pretty fast-and-loose with entropy, but it is magic, although the difference in entropy may factor in as a loss in efficiency.) There is also a range limit, with "lost" energy dissipating as heat between the magic user and the target. (Basically, at a distance $D$ from the target, the magic user must spend $2x$ energy to apply $x$ to the target, with the other $x$ getting lost somewhere en route, possibly as infrared radiation.)
To phrase this a little differently... magic is a lot like a combination of Newton's Cradle — a moving ball strikes a stationary mass in an inelastic collision, and the energy is transferred through the mass (without the stationary mass moving itself) to another ball — and a "super ball" — an object which, upon striking an "immovable" object, rebounds in a perfectly elastic collision such that its speed remains constant but the direction of its motion changes. All (my story's) magic brings to the party is that these effects are combined, i.e. it is like a Newton's Cradle where the stationary mass is immaterial (and can transfer energy/force through other matter occupying the same space as the immaterial "mass" with minimal effect on said matter), and can redirect the force in a different direction. (Propagation is presumably still subject to the speed of light, but for my purposes this is effectively negligible; magic only works over short distances.)
Now... it also seems like the reverse of heating things should be possible. After all, cooling is just applying an acceleration to atoms in opposition to those atoms' present velocity, and we certainly have technological means of cooling things (note the referenced question and answers thereto).
The problem is that this appears to violate thermodynamics; we can't just decrease the entropy of the universe. In particular, the "naïve" solution would be to postulate that the metabolic energy produced by the magic user perfectly counteracts the existing atomic motion of the target to be cooled, but this implies that the user's metabolism produces $k$ energy which doesn't just not affect the user directly, but effectively vanishes from the target. IOW, I just removed $2k$ energy from the universe (and incarnated Maxwell's Demon in the process).
How can I avoid violating thermodynamics in this manner, but still allow magic to cool things? I'm looking particularly for answers that can quantify how much heat needs to be dumped elsewhere (presumably into the magic user's body and/or surroundings).