Context. A hot vortex formed in the stratosphere of Saturn following the 2010-2011 Northern Storm. Huge temperature increases have been measured in the vortex around the millibar level. Enhancements in hydrocarbon abundances have been observed at the millibar level in 2011-2012 inside this vortex. Aims: We model the time-dependent photochemistry inside the vortex by accounting for the temperature variability over the period from January 2011 to March 2012 to assess whether photochemistry alone can explain the enhancements seen in the hydrocarbon abundances. Methods: We used a 1D time-dependent photochemical model of Saturn and adapted it to the perturbed conditions of the vortex after validating it in quiescent conditions. Results: Our model predicts non-variability for ethane (C2H6) and acetylene (C2H2) and an increase in ethylene (C2H4) by a factor of 3 in the mbar region. Heavier hydrocarbons show a stronger variability than the lighter ones. We are unable to reproduce the increase seen in C2H2 , and we significantly underestimate the increase seen in C2H4. Conclusions: Pure photochemistry does not explain the variability seen in the abundance of most hydrocarbons. This means that dynamics (eddy diffusion and/or advection) must have played a significant role in shaping the vertical profiles of the main hydrocarbons.