  We study the dynamics of cosmological phase transitions in the case of small
velocities of bubble walls, $v_w<0.1$. We discuss the conditions in which this
scenario arises in a physical model, and we compute the development of the
phase transition. We consider different kinds of approximations and refinements
for relevant aspects of the dynamics, such as the dependence of the wall
velocity on hydrodynamics, the distribution of the latent heat, and the
variation of the nucleation rate. Although in this case the common
simplifications of a constant wall velocity and an exponential nucleation rate
break down due to reheating, we show that a delta-function rate and a velocity
which depends linearly on the temperature give a good description of the
dynamics and allow to solve the evolution analytically. We also consider a
Gaussian nucleation rate, which gives a more precise result for the bubble size
distribution. We discuss the implications for the computation of cosmic
remnants.
