You only need the heat mat to germinate the seeds.
Not all seeds need that extra warmth, so you don't need to use the heat mat for everything. There are a couple of websites around with lists of the optimal temperatures for germinating seeds, here's one:
http://tomclothier.hort.net/page11.html
Once the seedlings are up, you can remove the heat mat. Most seedlings do better in cooler temperatures than were needed for the seeds to sprout.