If the tempera cakes in question are in a tray, I don't think there is any remedy for
cleaning other than one cake at a time. A couple of remedies come to mind:
1. Wet the tray with water and let sit for a couple of minutes. Wipe out each
cake with a paper towel, and they should come clean.
2. If the cakes are REALLY gross, wet them and wipe out with a scrubbing pad
(those green things from the cafeteria) as with the paper towel.
3. To maintain the trays, I have been successful taking the whole tray to the sink
and, starting at the end with the lighter colors, rinse the whole thing down. This
really works after you have had kids working with the paints and they are already
moistened. Lay them out to dry somewhere, and you've got it licked! (figure of
speech, I'm not recommending actually licking them!)