This theoretical study explores the influence of inertia, surface tension, and viscous dissipation on the transient heat transfer during the growth and collapse of fluid shells. The shell is spherical, the fluid is Newtonian, and the flow is induced by a constant driving pressure. The coupled heat and flow equations are solved numerically using the Cobody (Lagrangian) transformation, and a central difference discretization in space. The results are described in terms of four dimensionless numbers, namely, the Reynolds number, the capillary number, the Peclet number and the Brinkman number. In particular, it is found that viscous dissipation and surface tension have a significant effect on the temperature evolution within the fluid, namely on the temperature buildup within the fluid shell.