I'd give it a go, except for the fact that most dishwashers are a cold-water fill, and have a heater to heat the water to probably around the same temp that your home hot water heater produces. The reason for the heater in the dishwasher is twofold - it helps sterilize the dishes and also helps dry them afterwards.
I'd hate to see the fuselage and wings of a 1/48 scale Catalina after they've been in the dishwasher - can you say "curvy"??
Some dishwashers are a hot-water fill (like mine), and pull water straight out of your hot water heater. If you can't put your hands in the water because of the temperature, it's too hot for styrene.
But good luck anyway.
I'll stick to hand washing my plastic in warm water.
Cheers!
LeeTree