I find this all a bit odd, I have fitted literally thousands of bearings, in nearly forty years in engineering, and have never heated a bearing in my life! Not saying you shouldn't do it, but you certainly couldn't do it with the modern "sealed for life" bearings, it would melt the grease out. I would just cool the shaft in a freezer if you could get it in, or press fit the bearing on a press. If the shaft is machined to the correct interference size, there shouldn't be a problem.
You can fit a bearing quite safely with a hammer, but you dont "beat the heck out of it" you use a peice of tube that matches the diameter of the inner race, and tap it on with a 2lb hammer.
Angus, the most common problem which scraps a dishwasher is the water softener (where you put the salt in) reaches the end of its life. Ask at your local independant appliance retailer, as they have to take them in for recycling, and the "big boys" like Curry's etc won't like breaking company policy to give you an old one. It would keep you out of trouble with the wife too!
Phil.UK