Unless new, I would probably replace the battery next chance I got anyway. While this could just be a fluke, the fact the problem occurred overnight (when the computer is off for hours), might indicate a weak or failing battery. If not a bad battery, you are only out a couple bucks. Just make sure you unplug from the wall and touch bare metal of the case interior before reaching in and pulling and replacing the battery. It is typically a CR2032 wafer battery, available at most any watch/camera/battery counter. Take the old battery with you as most counters recycle.
Also, in spite of long time rumors to the contrary, you only need remove the battery for 10 or 15 seconds (or move CMOS reset jumper for 1 or 2 seconds). The CMOS circuit is intentionally designed to be reset easily and that is exactly why engineers selected CMOS memory modules instead of less volatile memory types, like EEPROMs. Of course, there's no harm waiting longer and 15 seconds does not give you time to watch Married with Children.
I haven't looked inside the case since I installed the new hard drive (6 months to a year ago)
I generally recommend monthly inspections, cleaning when necessary. 6 months of case fans sucking dust and cat hair (the worst due to sticky oils) into the case is a long time before cleaning. This, of course, varies with every computer based on hours per day running, number of fans, nearby foot traffic stirring up dust, kids and animals, cookie crumbs, etc., so inspection intervals can be adjusted once cleaning intervals are determined.
Oh - and because cleaning is a PITA, all my builds use cases with removable, washable air filters.
Even after letting it cool it idled around 65c!
Cleaning and repasting problem solved...
Yeah, I get nervous when CPU temps touch, and stay above 60°C. Note if not covered by a layer of heat trapping dust, and if the CPU fan is spinning properly, then high CPU temps indicate inadequate case cooling (assuming no overclocking) and perhaps additional or upgraded (larger) fans are needed.
By "repasting", do you mean you re-applied a new layer of TIM (thermal interface material)? Note TIM does not get old, go bad or wear out on its own and easily will last, and remain effective for 10 years or more as long as
the cured bond between the heatsink and CPU die is not broken. It may get and look a little crusty around the exposed edges, but between the mating surfaces, all is good. I mention this because the potential of ESD damage and incorrect mounting is much greater whenever you remove the heatsink.