Systems and methods for preventing or reducing unwanted heat in a microfluidic device while generating heat in selected regions of the device are described. Current can be supplied to a heating element through electric leads that are designed so that the current density in the leads is substantially lower than the current density in the heating element. Unwanted heat in the microfluidic complex can be reduced by thermally isolating the electric leads from the microfluidic complex by, for example, running each lead directly away from the microfluidic complex. Unwanted heat can be removed from selected regions of the microfluidic complex using one or more cooling devices.