We present a technique to locally and rapidly heat water drops in microfluidic devices with microwave dielectric heating. Water absorbs microwave power more efficiently than polymers, glass, and oils due to its permanent molecular dipole moment that has large dielectric loss at GHz frequencies. The relevant heat capacity of the system is a single thermally isolated picolitre-scale drop of water, enabling very fast thermal cycling. We demonstrate microwave dielectric heating in a microfluidic device that integrates a flow-focusing drop maker, drop splitters, and metal electrodes to locally deliver microwave power from an inexpensive, commercially available 3.0 GHz source and amplifier. The temperature change of the drops is measured by observing the temperature dependent fluorescence intensity of cadmium selenide nanocrystals suspended in the water drops. We demonstrate characteristic heating times as short as 15 ms to steady-state temperature changes as large as 30 degrees C above the base temperature of the microfluidic device. Many common biological and chemical applications require rapid and local control of temperature and can benefit from this new technique.