  A high-resolution calorimetric study has been carried out on nano-colloidal
dispersions of aerosils in the liquid crystal
4-\textit{n}-pentylphenylthiol-4'-\textit{n}-octyloxybenzoate ($\bar{8}$S5) as
a function of aerosil concentration and temperature spanning the
smectic-\textit{C} to nematic phases. Over this temperature range, this liquid
crystal possesses two continuous XY phase transitions: a fluctuation dominated
nematic to smectic-\textit{A} transition with $\alpha \approx \alpha_{XY} =
-0.013$ and a mean-field smectic-\textit{A} to smectic-\textit{C} transition.
The effective critical character of the \textit{N}-Sm\textit{A} transition
remains unchanged over the entire range of introduced quenched random disorder
while the peak height and enthalpy can be well described by considering a
cut-off length scale to the quasi-critical fluctuations. The robust nature of
the \textit{N}-Sm\textit{A} transition in this system contrasts with
cyanobiphenyl-aerosil systems and may be due to the mesogens being non-polar
and having a long nematic range. The character of the Sm\textit{A}-Sm\textit{C}
transition changes gradually with increasing disorder but remains
mean-field-like. The heat capacity maximum at the Sm\textit{A}-Sm\textit{C}
transition scales as $\rho_S^{-0.5}$ with an apparent evolution from
tricritical to a simple mean-field step behavior. These results may be
generally understood as a stiffening of the liquid crystal (both the nematic
elasticity as well as the smectic layer compression modulus $B$) with silica
density.
