The discussion was getting carried away, so here we go:
Polyurethane is very heat resistant -62°C to 93°C with special formulations able to handle temps as high as 150°C, however that's in a solid, cast or molded form.
All other search results I've looked at for "heat resistant polyurethane wood finish" come up with concerns about putting hot items directly from the stove or oven on a woodworking-finish polyurethane-coated table. This Woodworking.SE answer, however, indicates that a poly coat may have been what was used on the question's table that was, in fact, cooking-hot pot heat resistant for several decades.
Considering that the internal case temperatures aren't likely to be anywhere near those of a pot off the stove or casserole dish out of the oven, I'd think that it's quite likely that your finish will hold up to temps into the 40°C range for quite some time.
Alternatively, you are considering an epoxy coating. Epoxy can be had in quite a number of formulations, including very high temperature resistant ones, so it's a simple matter of choosing one that suits your expected conditions. According to this site:
Unfortunately, epoxy resin is not heat resistant. Epoxy resin can only withstand heat up to 302°F. Fortunately, there are many types of hard-curing resins, and each has a different degree of heat resistance.
Note that epoxy can "only" withstand temps up to 302°F (150°C) and that's a fair bit above what your computer components will produce. Right out of the box with epoxy you're at the upper end of what polyurethane can take so you probably won't need to look for any sort of special heat-resistant epoxy coatings - just about any common wood working epoxy should do the trick.
According to this site:
Mold, Mildew & Fungus Resistance
Most polyether based polyurethanes do not support fungal, mold and mildew growth and are therefore highly suitable for tropical environments. Special additives can also be added to reduce this in polyester materials as well.
To be honest, I don't know if polyurethane based wood finishes are polyether based, so it would be wise to do some research on the particular brand you're considering. By "doing research", I really mean "contact the vendor and explicitly ask", as that would get you the most accurate answer. However, it does appear that most PU finishes are mold resistant, so that shouldn't be a concern for you either.
According to this site:
Master Bond epoxy systems are non-nutrient and do not sustain or support mildew/mold/fungi or biological growth.
Now, this specifically talks about one brand of epoxy, but note that it says "non-nutrient". I can't imagine that there are any ingredients in any epoxy formulation that would actively support the growth of mold. (I take this claim to be much like the "Gluten Free!" label on a package of bacon. Gluten is from wheat, and there shouldn't be any wheat product in bacon.)
Of course, no matter what coating you use, if there are mold spores in the air, they can land on any surface and if they get enough humidity and enough nutrients landing on them from other airborne sources, mold will grow. However, there's no indication that either polyurethane or epoxy will directly support mold growth any more than a piece of steel would.
This indicates that neither heat nor mold resistance are going to be significant concerns for your computer case. Therefore, you're free to choose your finish treatment as you desire without worry about either of these concerns.
One thing that you should be concerned about but didn't bring up is that MDF is exceptionally vulnerable to water. Anything more than average humidity exposure will cause the MDF to absorb moisture and start to swell. Once this happens, your material is shot and it's time to replace it - there's no repairing swollen MDF. This leads to a decision that provides the most water resistance for the MDF and that would, I would think, point me toward epoxy rather than poly.
Another concern is that MDF is not a particularly pretty material to work with and you'll probably want to hide it. Polyurethane coatings are, basically, clear (slightly yellowing, but basically clear). This has the tremendous disadvantage of showing off the bland MDF below. Epoxy, on the other hand, can be had (or made) in a multitude of colors, allowing you to hide the material beneath, even allowing you to match the case to your decor, should you desire.
All in all, I would use a colored epoxy for this situation, however, that's down to an aesthetic choice which is opinion based and, therefore off-topic for a question here. Functionally, I think either material would work well with a slight advantage to the epoxy.
Note: No endorsement of any of the web sites used as references or their products is implied or intended. They were chosen solely based upon their order of appearance in search results and for their ability to supply supporting data.