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}-Smtextit{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}-Smtextit{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 Smtextit{A}-Smtextit{C} transition changes gradually with increasing disorder but remains mean-field-like. The heat capacity maximum at the Smtextit{A}-Smtextit{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.
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