When I wash small pieces I put them in a very large Tupperware bowl filled with water and a few drops of Dawn dishwashing liquid. I let them soak until they are fully wet then I dump the water and fill it again with clean water--I do this until the water is clean.
Then I take the pieces and lay them flat on a towel and roll it up (the same way you would with a sweater), like a jelly roll, to get the excess water out. I iron them dry and have never had any problem with scorching them.
I usually do them in batches of same color families. If any of the fabrics are bleeding color I keep rinsing them until the water is clear. I usually watch TV while doing this so it isn't so boring. Actually, I find it sort of relaxing.