  We solve the nonperturbative renormalization-group flow equations for the
two-dimensional XY model at the truncation level of the (complete) second-order
derivative expansion. We compute the thermodynamic properties in the
high-temperature phase and compare the non-universal features specific to the
XY model with results from Monte Carlo simulations. In particular, we study the
position and magnitude of the specific heat peak as a function of temperature.
The obtained results compare well with Monte Carlo simulations. We additionally
gauge the accuracy of simplified nonperturbative renormalization-group
treatments relying on $\phi^4$-type truncations. Our computation indicates that
such an approximation is insufficient in the high-$T$ phase and a correct
analysis of the specific heat profile requires account of an infinite number of
interaction vertices.
