  The effect of the temperature evolution of QGP on its thermal conductivity
and elliptic flow is investigated here in the presence of a time-varying
magnetic field. Thermal conductivity plays a vital role in the cooling rate of
the medium or its temperature evolution. The magnetic field produced during the
early stages of (non-central) heavy-ion collisions decays with time, where
electrical conductivity plays a significant role. As the medium expands, the
electrical and thermal properties change, reflecting the effect in various
observables. In this study, we have calculated the thermal conductivity of the
QGP medium, incorporating the effects of temperature and magnetic field
evolution. We discovered that conductivity significantly depends on the cooling
rate, and its value increases due to temperature evolution. Furthermore, the
influence of these evolutions on the elliptic flow coefficient is measured, and
elliptic flow decreases due to the evolution. We also extend our study for the
case of Gubser flow, where, along with the longitudinal Bjorken expansion, the
radially transverse expansion is also present.
