  Heterogeneous superconductivity onset is a common phenomenon in high-$T_c$
superconductors of both the cuprate and iron-based families. It is manifested
by a fairly wide transition from the metallic to zero-resistance state.
Usually, in these strongly anisotropic materials, superconductivity (SC) first
appears as isolated domains. This leads to anisotropic excess conductivity
above $T_c$, and the transport measurements provide valuable information about
the SC domain structure deep within the sample. In bulk samples, this
anisotropic SC onset gives an approximate average shape of SC grains, while in
thin samples it also indicates the average size of SC grains. In this work,
both interlayer and intralayer resistivity are measured as a function of
temperature in FeSe samples of various thickness. To measure the interlayer
resistivity, FeSe mesa structures oriented across the layers were fabricated
using FIB. As the sample thickness decreases, a significant increase in
superconducting transition temperature $T_c$ is observed : $T_c$ raises from 8
K in bulk material to 12 K in microbridges of thickness $\sim 40$ nm. We apply
analytical and numerical calculations to analyze these and earlier data and
find the aspect ratio and size of the SC domains in FeSe consistent with our
resistivity and diamagnetic response measurements. We propose a simple and
fairly accurate method for estimating the aspect ratio of SC domains from $T_c$
anisotropy in samples of various small thickness. The relationship between
nematic and superconducting domains in FeSe is discussed. We also generalize
the analytical formulas for conductivity in heterogeneous anisotropic
superconductors to the case of elongated SC domains of two perpendicular
orientations with equal volume fractions, corresponding to the nematic domain
structure in various Fe-based superconductors.
