We perform spatially dependent tuning of a GaInP photonic crystal cavity using a continuous wave violet laser. Local tuning is obtained by laser heating of the photonic crystal membrane. The cavity resonance shift is measured for different pump positions and for two ambient gases: He and N-2. We find that the width of the temperature profile induced in the membrane depends strongly on the thermal conductivity of the ambient gas. For He gas, a narrow spatial width of the temperature profile of 2.8 mu m is predicted and verified in experiment. (C) 2015 AIP Publishing LLC.