  Aims. The interaction of two isotropic stellar winds is studied in order to
calculate the free-free emission from the wind collision region. The effects of
the binary separation and the wind momentum ratio on the emission from the
wind-wind interaction region are investigated. Methods. We developed a
semi-analytical model for calculating the thermal emission from colliding
stellar winds. Assuming radiative shocks for the compressed layer, which are
expected in close binaries, we obtained the emission measure of the thin shell.
Then, we computed the total optical depth along each line of sight to obtain
the emission from the whole configuration. Results. Here, we present
predictions of the free-free emission at radio frequencies from analytic,
radiative shock models in colliding wind binaries. It is shown that the
emission from the wind collision region mainly arises from the optically thick
region of the compressed layer and scales as ~ D^{4/5}, where D is the binary
separation. The predicted flux density from the wind collision region becomes
more important as the frequency increases, showing higher spectral indices than
the expected 0.6 value from the unshocked winds. We also investigate the
emission from short-period WR+O systems calculated with our analytic
formulation. In particular, we apply the model to the binary systems WR 98 and
WR 113 and compare our results with the observations. Our theoretical results
are in good agreement with the observed thermal spectra from these sources.
