The second harmonic of an infrared laser generated by frequency doubling in a nonlinear crystal can be adversely affected by group delay dispersion applied to the fundamental radiation. Yet large amounts of group delay dispersion can be advantageous when using periodically poled crystals with a linearly chirped period. We propose to achieve the same effects with continuous variation of the phase mismatch in the propagation direction, by applying a temperature gradient to a lithium triborate crystal. Advantageously the temperature gradient can be adjusted depending on the desired results. We demonstrate, through both simulation and experiment, an improvement in not only second harmonic conversion efficiency and beam quality, but also that the second harmonic duration and is bandwidth can be controlled with the temperature gradient.