How do I increase the drive current from the arduino digital pins?
You will have to use a transistor to drive the heatplate.

Something similar to this:







simulate this circuit &ndash; Schematic created using CircuitLab

Note that this is a simplified general circuit. Without knowing the specs of the load you are trying to drive, we can't specify which components to use.



EDIT:
Based on your info of the voltage of the load's supply and that you already have a TIP120 to switch its power, consider this circuit that I found in this site. As @Matt pointed, a flyback diode will not hurt anybody.







simulate this circuit