The Curie temperature ${T}_{c}$ of ferromagnetic ${\mathrm{La}}_{0.7}{\mathrm{A}}_{0.3}{\mathrm{CoO}}_{3}$ ($A=\mathrm{Ca}$, Sr, Ba) thin films was studied as a function of the film thickness $d$ for $400\phantom{\rule{0.3em}{0ex}}\mathrm{nm}>d\ensuremath{\geqslant}2.6\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. A finite-size shift of the critical temperature relative to the bulk value, $1\ensuremath{-}{T}_{c}(d)∕{T}_{c}(\mathrm{\ensuremath{\infty}})\ensuremath{\propto}{d}^{\ensuremath{-}\ensuremath{\lambda}}$, with a constant critical shift exponent of $\ensuremath{\lambda}\ensuremath{\approx}1$ over the entire thickness range was observed. This value of $\ensuremath{\lambda}$ is rather unusual for thick films $(d>100\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ and normally expected for two-dimensional magnetic structures (i.e., ultrathin magnetic films with a thickness of a few monolayers) or spin-glass systems. Measurements of the magnetoresistivity reveal spin-dependent variable range hopping in the ultrathin films, which is strongly suppressed with increasing film thickness by percolation. The occurrence of charge-carrier localization and spin-misorientation hints to an exchange interaction between isovalent Co ions and thus to a phase-separation of ferromagnetic and antiferromagnetic regions, which may be the reason for the observed unusual critical shift exponent $\ensuremath{\lambda}$.