[brainanator]

If they are all wired in parallel as you described (as in, not "daisy chained" but each one going to the power source individually) then they are ALL getting the full voltage. You can't add up the voltage drops (like you did with 1.5*12=18). If theyare all in series (one after the other) you can do that.
I don't think each one has a diode, since LEDs ARE diodes (light emitting diode). They might have a built in resistor, which is why you haven't blown them up yet. LEDs usually don't warm up on there own unless they are very high powered. And then not enough to melt hot glue.

Without knowing exactly what you have it's hard to know what advice to give you. This secondary component is what's saving them, otherwise plugging straight into 21V would surely fry them right away.