I was hoping that weed seeds in my small, cold pile would sprout and die, or rot and die, or be eaten by worms and die ... but not last year!
I have a 5 gallon bucket of compost left over from last year - I stopped using it when I realized that I was just sowing weeds when I top-dressed with it. It's probably better to mulch over compost anyway, to keep it moist.
I think I'll use it in a bed that already is as weedy as it can possibly be, but turn it under and consider the weeds that sprout anyway as "green manure" or a cover crop, and just chop them into the soil as they sprout. BEFORE they go to seed!