  This paper is the third in a series, studying the optical properties of a
sample of mid-IR Warm Seyfert galaxies and of a control sample of mid-IR Cold
galaxies. The present paper is devoted to surface photometry. We analyse the
light distributions characterizing the galaxies outside the central 2 kpc. The
radial light profiles are decomposed, using two generalized exponentials, in
inner and outer components. Each is characterized by the profile shape, central
surface brightness and scale length. We find that light is more centrally
concentrated in Seyfert 1s, that also tend to lie in earlier-type hosts than
Seyfert 2s. Seyfert 1 and 2 bulges have similar shapes but the former are
characterized by larger central surface brightnesses and smaller scale lengths.
The three parameters characterizing the bulge component correlate with each
other, within a limited range of bulge luminosities. Cold galaxies are
disk-dominated systems, with complex morphologies. Their bulges are flatter and
fainter compared to the Warm sample. The disk structural parameters span
similar ranges for the three (sub)samples but with larger scatter. The
parametrization of light profiles, as described in this paper, shows that the
three (sub)samples occupy different loci in parameter space, that is suggestive
of an evolutionary connection between them.
