In the present work, dynamics of a bubble rising in temperature varying viscous stratified fluid medium is studied numerically. Effect of linearly and exponentially varying temperature-dependent viscosity on bubble rise dynamics is studied and compared with that of temperature independent viscosity fluid medium. The behavior of bubble rise and its shape evolution are examined for four different sets of Reynolds number and Weber number values, for all three types of viscosity variations. At lower Reynolds number values, surface tension plays a major role on the shape of the bubble forming into an oblate or elliptical shape, and bubble rise velocity is found to be higher for temperature independent viscosity case, whereas, at higher Reynolds number values, shape of the bubble deforms and forms into elongated oblate or skirted shape bubbles. The bubble rise velocity showed oscillation in the initial stage of bubble rise, whereas after reaching to its terminal shape, the oscillation of rise velocity dies down resulting into terminal velocity. Overall, the terminal velocity of the bubble is found to be diminished in temperature-dependent viscosity-stratified fluid medium compared to that of in constant viscosity fluid medium.