Miniaturized laboratory-on-chip systems promise rapid, sensitive, and multiplexed detection of biological samples for medical diagnostics, drug discovery, and high-throughput screening. Within miniaturized laboratory-on-chips, static and dynamic droplets of fluids in different immiscible media have been used as individual vessels to perform biochemical reactions and confine the products. Approaches to perform localized heating of these individual subnanoliter droplets can allow for new applications that require parallel, time-, and space-multiplex reactions on a single integrated circuit. Our method positions droplets on an array of individual silicon microwave heaters on chip to precisely control the temperature of droplets-in-air, allowing us to perform biochemical reactions, including DNA melting and detection of single base mismatches. We also demonstrate that ssDNA probe molecules can be placed on heaters in solution, dried, and then rehydrated by ssDNA target molecules in droplets for hybridization and detection. This platform enables many applications in droplets including hybridization of low copy number DNA molecules, lysing of single cells, interrogation of ligand-receptor interactions, and rapid temperature cycling for amplification of DNA molecules.