I believe that I can call myself an expert here, since I have more than 30 experience in construction, and my speciality happens to be HVAC design, both residential and commercial. My degrees are in mathematics and electrical engineering, which I got before going into construction. I had originally planned to design semiconductors, but with the price pressure put on them by the Japanese in the 1980's, jobs in that area were hard to come by for a while, which is why I changed fields. I work for a small contracting company today, and have worked for large firms in the past. I consider myself to be an expert in Manual J heat load calculations, which I can still do without the aid of a computer (I hated my thermo class in school, though - LOL).
NOTE: Although I consider myself to be a musician, and a good one too, my day job is what pays the bills, and never quit it. I know musicians who have quit their day jobs, and although some did OK, others ended up in a world of hurt. Not me. I was a coward. LOL.
With 30 years plus of experience in the HVAC industry (my day job), I can tell you for a fact that the hotel is entirely within their right. When designing a building, heat loads are calculated, and these heat loads are for normal occupancy. A heat load design must be passed by whichever governmental entity has jurisdiction in that area. This is done before ground is even broken for construction. Once the system is installed, it is then inspected, and passed if it meets the building code. A designer cannot design an A/C system for the kind of occupancy that existed at the Trump event. If he did, the system would cool off so fast that it would not remove moisture (latent heat) from the air, and you would end up with mold and high humidity inside the building. It would also not pass building code for that very reason. A properly designed commercial system will make the space it was designed for 20-25 degrees cooler than the outside (ambient) temperature. With an unusually large number of people in a room, it is going to be less, due to the heat generated by persons (330 BTUH per person in the room, along with a little extra latent heat per person, in the form of humidity). That significantly adds to the heat load. With a seasonally high ambient temperature, the temperature at which an HVAC system is going to be able to get to is going to be less. There are 2 facets to this. 1) Higher outside ambient temperature means a higher temperature inside and 2) More people than the system was designed to handle means a lower temperature drop. Temperature drop is the delta from the average temperature at the return grilles to the average temperature at the supply grilles. The people load is in addition to the load created by electronics, lights, and other heat generating sources in the space being conditioned. These all contribute to the part of the load that can interfere with temperature drop if an abnormally large load is created. NOTE: The figures I gave are for the Houston Texas area. In other parts of the country, a system may be able to drop the temperature a few extra degrees, due to less ambient humidity (latent heat). However, the physics is still the same.
Since Donald Trump is a general commercial contractor, he is going to know this. Actually, he is required to know this if he is competent at what he does. I assume that Donald Trump is competent. Therefore, Donald Trump was hinting at a way he might attempt to stiff the hotel out of their rightfully deserved pay.