We describe the work carried out to obtain observational evidence of a local relation between the temperature and the magnetic field in different regions of several sunspots. Information about the temperature is extracted from the continuum intensity. The magnetic field is deduced by using the Stokes V profile of lines with different excitation potentials. A scaling relation between Stokes V and continuum intensity is used to estimate the stray-light contamination. The observed local relation between continuum intensity and magnetic field can be adapted to the equations describing magnetostatic horizontal force balance. The commonly accepted value for the Wilson depression suggests that the tension forces are as important as the magnetic pressure in defining horizontal equilibrium. The local relation observed holds for spatial scales larger than 1 arcsec. Evidence of unresolved hot magnetic regions inside the umbra is presented. Our study provides clues pointing to a dependence of continuum intensity with sunspot area. Small spots are seen to be brighter than big ones.