L293D Getting Really Hot, Really Fast

That's always the fun part, as I have said before, I'm not farmilliar with this board, but I know that in some cases you have to get really creative. I have had to mill up my own aluminum sinks specially shaped and use a bit more thermal paste than I would like, but it works. Mostly tho, if the board was supposed to have a heatsink, it normally has some kind of provision for mounting it, even if that is just a small flat surface to "glue" it on the chip.