I am going to throw out somewhat of a frame challenge to this question.
'Heat' is not a separate 'thing'. Temperature is a property of matter, directly related to it's state (solid, liquid, gas). Without matter, there can be no temperature. 'Hot' and 'cold' are only artifacts in our mind, constructs to describe certain sensory information. Unfortunately, the terms 'heat', 'temperature', 'hot' and 'cold' are very often (still) confabulated into false or fake concepts.
Without some form of matter, there can be no temperature, no 'hot' or 'cold', any more than there can be a 'solid', 'liquid', or 'gas' without some form of matter. A vacuum in space can have no temperature, because there is no matter to apply this property to. In this sense, 'cold' is like talking about 'red'. There has to be something that has the property 'red'. The property 'red' in and of itself, in isolation, does not exist.
There can be no such thing as a 'cold ray' without there being some form of matter that the cold is a property of. This wizard has to be projecting some 'thing', some 'matter' (even be it 'ether') that has the property 'cold'.
There is another option. That is, the 'ray' does not go from the wizard to the object, but the reverse. Somehow, the spell is able to convert the vibrating heat energy of the molecules of the equipment into some form of EM energy, and beam that back to the staff, or the wizard can cast a spell that causes the layer of atmosphere surrounding the object to do the same (meaning this spell is worthless in space). The surrounding atmosphere would then, through conduction, draw heat out of the target. So, now the question that is begged to be asked is 'does the spell continue to draw energy out of the layer of atmosphere, or are normal principles of thermodynamics now to play out?'
Here, a brief history of thermodynamics that outlines the historical misconception of 'heat' in popular mythology..
Up until the mid-1800's, the concept of heat as a 'thing' prevailed. Just as fire was an element and not an artifact of combustion, somehow heat was some form of material or ether or some 'thing' that could move around of its own accord. It was not just a property of matter; it had an existence in and of itself. It is easy to see how they could have this concept, since most of their experiences with heat had something to do with it 'coming out of something', either logs in a fire, a volcano, or the Sun. When you burned a log, you liberated this thing called 'heat' and it was able to cook your food, destroy a building, or cause ice to melt. The concept of 'fire' as an 'element' that was released was very much a part of this. Fire and heat were mysteriously, mystically linked. Such ideas as the conservation of heat were unknown, because it seemed to be something that was extracted and then used up. When one got heat from a log, nothing got cooler.
This concept sufficed as an explanation right up to the invention of the steam engine. Not the invention of the engine itself, but the desire to optimize the work it could do. The time period around the 1850's was marked by a tremendous competition between England and France into the mastery and perfection of this technology and the idea that work could be obtained from the transfer of heat. It is not just a coincidence that the theories of thermodynamics of Carnot, Maxwell, August Krönig, Ludwig Boltzmann and Rudolf Clausius among others came about in this time period. It was all about the power of steam to build a strong industrial base. The country that mastered it would be the dominant driver, and it was a national priority to understand it. The age of mastery over steam, in many respects, provided the impetuous for the age of physics. There was unabashed support at the governmental level for any research into it.
The work of Clausius, in particular, building on Carnot, developed the idea that heat was something that flowed from a high heat pressure (high temperature hot) to a low heat pressure (low temperature cold), and thus what was hot became cooler, what was cold became hotter, until equilibrium was reached. But what about the log that produced this heat? Where in the log did it come from? The log got smaller as heat came from it. Where does conservation of matter come in? It is obvious the log is being destroyed. (Of course, the idea of using the term 'pressure differentials' was not directly referenced, full apologies to Boyle, and even Boyle did not relate gas pressures to 'vibrating moving atoms' colliding, Rutherford having not yet been born).
But even though during this period the world of physics moved closer and closer to the understanding that heat was a property of matter, not something distinct from matter, and the kinetic theory of gasses took shape, it was not quite there yet. Heat was regarded as a means to an end, and that end was work. To Maxwell and others, heat that was created or released or produced from combustion, and not used to do real work, was a waste and contributed to inefficiency. Heat energy was conserved once it was released, and then moved from the air to water and steam, but the energy not converted to work was lost, never to be recovered again. How to console this alleged reality with the laws of conservation of matter and energy? The solution, of course, was this misdirection called 'entropy' that became a term physicists bandied about, changed the definition to suit, used to patch the holes in the theories, and thus allowed then to go to sleep at nights.
It was not until Rutherford, and the beginnings of the understanding that heat was a measure of the vibrations of atoms, did heat begin to become a 'property of matter'. The idea of the kinetic theory of heat truly matured. There was no separate 'thing' or 'energy' or 'heat' that existed, except that it was an inherent property or result of the vibration of atoms that made up matter. Without these atoms vibrating, there was no heat.