You don't have to drain ALL the coolant, just enough to get the level below where you're going to be working. If your radiator petcock works (often they're rusted closed), you're in luck, just drain into an empty antifreeze jug, probably a gallon should do it. You didn't mention whether it was where the top half of the housing attaches to the bottom half, or where the bottom half attaches to the head? In any case, don't forget the round rubber gasket that goes on top of the thermostat! This gasket (o-ring in Toyota parts jargon) prevents coolant from bypassing the thermostat when it's supposed to be closed.
These are easy gaskets to replace, but hard to scrape the old gasket and gunga off the old surfaces. Also, do NOT overtighten the two bolts that hold the top half of the housing onto the bottom half, it's easy to strip the alloy (don't ask me how I know this :-)