You can try a heat sink to start with, though in our tests that only allows the current to increase by a small amount (100mA or so).
If you look at some robot/hobby stores there are lots of motor drivers to choose from in a variety of current ratings. Here's an L298 product at a shop in Denmark that already seems to have a heatsink attached.
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The Quick Shield: breakout all 28 pins to quick-connect terminals