Recently, the iridate double perovskite ${\mathrm{Sr}}_{2}{\mathrm{YIrO}}_{6}$ has attracted considerable attention due to the report of unexpected magnetism in this ${\mathrm{Ir}}^{5+}$ $(5{d}^{4})$ material, in which according to the ${J}_{\mathrm{eff}}$ model, a nonmagnetic ground state is expected. However, in recent works on polycrystalline samples of the series ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{YIrO}}_{6}$ no indication of magnetic transitions have been found. We present a structural, magnetic, and thermodynamic characterization of ${\mathrm{Sr}}_{2}{\mathrm{YIrO}}_{6}$ single crystals, with emphasis on the temperature and magnetic field dependence of the specific heat. As determined by x-ray diffraction, the ${\mathrm{Sr}}_{2}{\mathrm{YIrO}}_{6}$ single crystals have a cubic structure, with space group $Fm\overline{3}m$. In agreement with the expected nonmagnetic ground state of ${\mathrm{Ir}}^{5+}$ $({5d}^{4})$ in ${\mathrm{Sr}}_{2}{\mathrm{YIrO}}_{6}$, no magnetic transition is observed down to 430 mK. Moreover, our results suggest that the low-temperature anomaly observed in the specific heat is not related to the onset of long-range magnetic order. Instead, it is identified as a Schottky anomaly caused by paramagnetic impurities present in the sample, of the order of $n\ensuremath{\sim}0.5(2)%$. These impurities lead to non-negligible spin correlations, which nonetheless, are not associated with long-range magnetic ordering.