I work as grower for a commercial greenhouse- have since I was 13yo- and agree that, even granting that most house plants are by nature tropical, cool temps by themselves aren't the problem. We routinely run our greenhouses in the 50s in the winter as a fuel- saving measure and most plants are just fine. In fact, when I do programs on the subject for a garden club I recommend keeping the plants as cool as the homeowner can stand. the reasons are twofold: first, cooler temps = higher relative humidity, which plants like; and second, because it slows down their growth rate. Indoor conditions in the winter suck- low light, low humidity, little air movement; any growth tends to be weak and spindly and probably will need to be pruned off in the spring.
I agree that your problem is probably water-related; however, IMO the oft-repeated mantra that overwatering kills more house plants than any other cause is bullshit. It implies that you as caretaker have nothing better to do than constantly pour water on your poor plants. In reality, excess soil water results from overpotting- using too big a pot- poor quality potting soil- a good soil mix will drain off whatever excess you put on- and/or lack of drainage in the container. If any of those conditions exist, I would nonetheless suggest waiting until spring to repot- after you see some sign of activity like new growth. BTW repotting may involve moving to a smaller pot if it seems way too big for the root ball. Until then err on the side of providing less rather than more water- even to the point of slight wilting.
Good luck!