The fraction of thermal (free-free) emission in the radio continuum at the frequency of 1.4 GHz is derived in 193 compact star-forming galaxies(CSFG). These galaxies with detected radio emission represent the subsample of a larger CSFG sample of about 14 000 galaxies (Izotov, Y.I., Guseva, N.G., Fricke, K.J., Henkel, C.: Mon. Not. R. Astron. Soc. 2016, 462, 4427) selected from the Data Release 12 of the Sloan Digital Sky Survey(SDSS) (Alam, S., et al.: Astrophys. J. Suppl. Ser. 219, 12, 2015). We use the 1.4 GHz fluxes from the FIRST (Becker R.H., White R.L., & Helfand D.J.: 1995, ApJ, 450, 559) and NVSS (Condon, J.J., Cotton, W.D., Greisen, E.W., et al.: 1998, AJ, 115, 1693) catalogues. The fluxes of the thermal component at 1.4 GHz are derived from the extinction- and aperture-corrected fluxes of the Hβ emission line in the SDSS spectra following to (Caplan, J., & Deharveng, L.: 1986, A&A, 155, 297) and are compared with the total fluxes in radio continuum. The distribution of the fraction of thermal emission A at 1.4 GHz is similar to the log-normal one. Its median values of 6 % and 14 % are derived respectively with the Hβemission line fluxes which are non-corrected and corrected for aperture. We consider these values as lower and upper limits and discuss their uncertainties introduced by aperture corrections. The derived fractions of thermal emission are similar to those found previously for different types of star-forming galaxies. We study the dependence of A on various parameters and find strong correlation with the equivalent width of the Hβ emission line W and the gr colour index I. The A value increases with increasing of the equivalent width W at a fixed colour index I or with increasing of the colour index I at a fixed equivalent width W. Additionally, we find that the fraction of thermal emission at 1.4 GHz is lower for older starbursts.