Hot room/baby

We currently live at my MILs house. Its a newer home (less than 10 years old?) And use to be the model home for the neighborhood. Our room was the office when it was a model home and is at the front of the house. The house has working AC, but for some reason our room will NOT get cool. I think it's poor insulation from our walls to the outside. We can feel the air turn on at the vent. Despite getting black out currents and a new vent, the room is still hot. We live in Texas and my baby is due at the end of July. I am so worried about it being too warm for him. We have a desk fan blowing on us that helps a lot. Its not miserably hot, but probably 75 degrees or so (which of course feels warm for a home) and im worried during summer heat it will be in the 80s. How can we keep baby cool? Will this be too hot for him? I am really stressed about it.