In this work, we explore the use of methods that allow a significant acceleration of genetic analysis within microchips fabricated from low thermal conductivity materials such as glass or polymers. Although these materials are highly suitable for integrating a number of genetic analysis techniques onto lab-on-a-chip devices, their low thermal conductivity limits the rate at which heat can be transferred and hence lowers the speed of thermal cycling. However, short thermal cycling times are the key to bringing PCR to clinical point-of-care applications. Although shrinking the PCR reaction chamber volume can increase the speed of thermal cycling, this strategy is not always suitable, particularly when dealing with clinical samples with low analyte concentrations. In the present work, we combine two alternate strategies for decreasing the time required to perform PCR: implementing a heat sink and optimizing the PCR protocol. First, the heat sink substantially reduces the thermal resistance opposing heat dissipation into the ambient environment, and eliminates the parasitic thermal capacitance of the regions in the microchip that do not require heating. The low thermal conductivity of glass is used to our advantage to design the heat-sink placement to achieve fast thermal transitions while maintaining low power consumption. Second, we explore the application of two-stage PCR to provide a further reduction in the time required to perform genetic amplification by merging the annealing and extension stages of the commonly used three-stage PCR approach. In combination, we reduce the time required to perform thermal cycling by roughly a factor of 3 while improving the temperature control.