Can a small window air conditioning unit be more cost effective than running central air in a house? I've moved into a new (old) house with central air conditioning, with the small master bedroom on the upper level of the house with windows facing south and west. I have a feeling this room is going to be very warm in the summer, even after I do some work with sun blocking the windows.

Would it make sense to install a 6000 BTU window air conditioning unit in that room to use while sleeping, rather than trying to cool the whole house sufficiently to cool that room? My plan would be to cool the bedroom to 72 degrees at night, let the rest of the house go up to 80 at night, then have the central air set at about 76 during the day.

Or does the combination of the expense of the unit ($350) plus the electricity to run it outweigh the cost of just letting the central unit do its job consistently throughout the day and night?

This may be impossible to answer with such little information to go on, but is this idea even worth considering? Or do people only do this out of necessity when the central unit can't cool the house adequately?