A theoretical model and its experimental realization for the temperature grating relaxation time constant and its impact on the temporal and the spectral profiles of a Q-switched and modelocked Nd:YAG laser pumped distributed feedback dye laser (DFDL) is reported. Boundary conditions for different types of excitation pulses have been established to predict the effect of temperature phase gratings on laser gain build-up and temporal elongation of the DFDL pulses. The proposed transient grating method is useful in measuring grating relaxation time constants for lasing dye solutions. The proposed mathematical model is demonstrated by measurement of the relaxation time constant of R6G in ethanol at 10-3M. The measured relaxation time constant of 16+/-0.2 ns is very close to the tabulated values determined using other techniques.