  We report electrical resistivity measurements on a high-quality
Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ thin film ($x=0.4$) under pressure. The
superconducting transition temperature (=39.95 K) of the optimally-doped thin
film shows a dome shape with pressure, reaching a maximal value 40.8 K at 11.8
kbar. The unusually high superconducting transition temperature and its
anomalous pressure dependence are ascribed to a lattice mismatch between the
LaAlO$_3$ substrate and the thin film. The local temperature exponent of the
resistivity ($n=d\text{ln}\Delta\rho/d\text{ln}T$) shows a funnel shape around
the optimal pressure, suggesting that fluctuations associated with the
anomalous normal state are responsible for high-temperature superconductivity.
