Saturn's axial tilt of 26.7{\deg} produces seasons in a similar way as on Earth. Both the stratospheric temperature and composition are affected by this latitudinally varying insolation along Saturn's orbital path. A new time dependent 2D photochemical model is presented to study the seasonal evolution of Saturn's stratospheric composition. This study focuses on the impact of the seasonally variable thermal field on the main stratospheric C2 hydrocarbon chemistry (C2H2 and C2H6) using a realistic radiative climate model. Meridional mixing and advective processes are implemented in the model but turned off in the present study for the sake of simplicity. The results are compared to a simple study case where a latitudinally and temporally steady thermal field is assumed. Our simulations suggest that, when the seasonally variable thermal field is accounted for, the downward diffusion of the seasonally produced hydrocarbons is faster due to the seasonal compression of the atmospheric column during winter. This effect increases with increasing latitudes which experience the most important thermal changes in the course of the seasons. The seasonal variability of C2H2 and C2H6 therefore persists at higher-pressure levels with a seasonally-variable thermal field. Cassini limb-observations of C2H2 and C2H6 (Guerlet et al., 2009) are reasonably well-reproduced from the equator to 40{\deg} in both hemispheres