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At some point tonight my power went out. Judging by the time on my alarm clock, it had been on for about an hour and a half when I got home.
My Aquaclear 50 was plugged in but making no noise. I tried unplugging it and nothing. I took it apart and cleaned everything. Noticed that the motor was very hot. Plugged it in and still nothing.
Will it work when it cools down or do I need to start looking for a filter sale?

Most likely the filter burned out. You can wait until the filter cools down to see if it works but if it doesn't you'll have to look into something new.

You might be able to just find replacement parts for it instead of replacing the entire filter.

Just as Spookster said, but that depends on what filter it is.

No hum at all if you fill it with water and plug it in? The power went out this past winter, and my Aquaclear 50 lost its prime but continued to try to work (made a grinding sound) until I got home and was able to prime it again. If you need parts contact the mfgr. (Hagen).