The stagnation dynamics of low temperature ignition targets consisting of bare deuterium-tritium (DT) fuels is described in terms of a non-adiabatic self-similar solution, which takes the energy dissipation due to bremsstrahlung into account. Without enough optical thickness, the radiation loss, which depends non-linearly on the background temperature and density, seriously affects the compression performance, and ignition fails. This feature sets a lower limit on the peak fuel parameter rho r for a given fuel mass. Accordingly, previous gain models, in which the calculation is launched at the moment of ignition assuming a fuel assembly at rest, are limited such that the maximum compressed state at lower rho r than the threshold is not expected to be realized through virtual stagnation