The out-of-plane coefficient of thermal expansion (CTE) measurement method, which is named the thermal bulge method, was used to measure the linear CTE values for freestanding nanocrystalline ultra-thin gold films with thicknesses ranging from 115 to 1200 nm. White light interferometry was used to determine the out-of-plane thermal deformation as a function of temperature. The thermal strain showed a linear behavior in the temperature range of 20 to $100^{circ}C$, but varied with the thickness (or grain size) of the specimen. The grain sizes, which were measured by transmission electron microscopy (TEM), showed a strong correlation with the CTE: Specimens with larger grain sizes (44 to 98 nm) had greater CTE values (9.6 to $13.6 ppm/^{circ}C$). Starting from the CTE values for fine-grained materials, the CTE of nanocrystalline gold films increased with increasing grain size and approached the CTE of bulk gold. The thermal bulge method, which was previously developed by the authors, allowed for direct, repetitive, reliable, and quick measurement of the CTE values of ultra-thin gold films.