YbBiPt is a heavy-fermion compound possessing significant short-range antiferromagnetic correlations below a temperature of $T^{textrm{*}}=0.7$ K, fragile antiferromagnetic order below $T_{rm{N}}=0.4$ K, a Kondo temperature of $T_{textrm{K}} approx1$ K, and crystalline-electric-field splitting on the order of $E/k_{textrm{B}}=1,textrm{-},10$ K. Whereas the compound has a face-centered-cubic lattice at ambient temperature, certain experimental data, particularly those from studies aimed at determining its crystalline-electric-field scheme, suggest that the lattice distorts at lower temperature. Here, we present results from high-resolution, high-energy x-ray diffraction experiments which show that, within our experimental resolution of $approx6,textrm{-},10times10^{-5}$ AA, no structural phase transition occurs between $T=1.5$ and $50$ K. In combination with results from dilatometry measurements, we further show that the compounds thermal expansion has a minimum at $approx18$ K and a region of negative thermal expansion for $9<T<18$ K. Despite diffraction patterns taken at $1.6$ K which indicate that the lattice is face-centered cubic and that the Yb resides on a crystallographic site with cubic point symmetry, we demonstrate that the linear thermal expansion may be modeled using crystalline-electric-field level schemes appropriate for Yb$^{3+}$ residing on a site with either cubic or less than cubic point symmetry.