Implementing precise time and space dependent heating and cooling in a microchip is potentially useful in a wide array of areas including reactions, separation, detection, etc. We present such a microchip, and understand the fundamental implications of the temperature changes on fluid flow and heat and mass transfer, while developing a chip that can perform rapid DNA amplification. It employs transparent Indium Tin Oxide (ITO) on a glass microchip to provide resistive heating capable of quickly and accurately cycling the temperature. In this approach the temperature is maintained constant spatially but is varied temporally. The bottom of the chip is kept cold in order to bring the temperature down quickly from the denaturing step to the annealing step. The rapid changes in temperature between the three stages, along with the speed of extension on such a small scale, result in less than 25 seconds per cycle. The chip was used to amplify H5 influenza DNA of 1776-bp. With this unique combination of temperature cycling, and pressure driven velocity results in amplicon having high yield and specificity. The effects of velocity and temperature cycling on DNA plug dispersion are explored.