  We present the results of a set of numerical simulations of long-duration
gamma-ray burst jets aimed at studying the effect of a variable engine on the
peak frequency of the photospheric emission. Our simulations follow the
propagation of the jet inside the progenitor star, its break-out, and the
subsequent expansion in the environment out to the photospheric radius. A
constant and two step-function models are considered for the engine luminosity.
We show that our synthetic light-curves follow a luminosity-peak frequency
correlation analogous to the Golenetskii correlation found in long-duration
gamma-ray burst observations. Within the parameter space explored, it appears
that the central engine luminosity profile does not have a significant effect
on the location of a gamma-ray burst in the Luminosity-peak frequency plane,
bursts from different central engines being indistinguishable from each other.
