It has always been my understanding that when it comes to instruments, particularly wood instruments, the rule of thumb is that what is comfortable for a person is what is comfortable for the instrument.
If it is cold or hot enough for you to feel uncomfortable then it probably isn’t the best environment for a harp.
Proper temperature takes a back seat to proper relative humidity. When the temperature changes then so does the relative humidity. I would say as a rule of thumb that colder is better than warmer, because lower temperatures RAISE relative humidity, and higher temperatures LOWER relative humidity.
Big changes in temperature are not good for the instrument, particularly very low temperatures(below 40 degrees F for example) that are then changed to much higher temperatures. Let’s say for example that your harp is in the back of the car in winter, where the temperature is maybe 40 degrees. If the harp is left there long enough, say over night, or on a 3 or 4 hour drive, then the whole harp descends to 40 degrees. There is nothing wrong so far. But, if you then take your 40 degree harp into a room that is say 70 degrees F, condensation will form on the instrument, including inside the action. This could do serious damage to the finish, metal parts and heaven knows what else. So it’s probably a good idea to try to keep the harp at a consistent temperature.
Unfortunately my young visitors sleeping in my harp room left the window open overnight recently and the outside temperature was about 4 to 5 degrees centigrade. Thankfully there is no apparent damage to the finish of the harps as the room rarely gets above 17 degrees in winter, they were covered with their dust covers and the room was not unbearably cold in the morning. However it’s a warning to me to ensure guests do not do this again. I think I suffered the greatest shock myself, worrying, but remarkably not one string broke that night, not even the frayed one.