How do I know if my element is the problem or the thermostate?

You need to test the resistance of the heater with a Volt Ohm Meter. Thermostat can be an on/off or possibly a proportional unit and harder to test. What is happening?

Here is a link that will be good for a few days: http://dl.dropbox.com/u/8010163/Whirlpool_Dishwasher.pdf
You need to follow the instructions in the booklet and test things with a meter before you change parts unless you can see it burned in two. Let us know how it works out.