Electronic and lattice contributions to picosecond time-resolved X-ray absorption spectra (trXAS) of CuO at the oxygen K-edge are analyzed by comparing trXAS spectra, recorded using excitation wavelengths of 355 nm and 532 nm, to steady-state, temperature-dependent XAS measurements. The trXAS spectra at pump-probe time-delays ≥150 ps are dominated by lattice heating effects. Insight into the temporal evolution of lattice temperature profiles on timescales up to 100s of nanoseconds after laser excitation are reported, on an absolute temperature scale, with a temporal sensitivity and a spatial selectivity on the order of 10s of picoseconds and 10s of nanometers, respectively, effectively establishing an "ultrafast thermometer". In particular, for the 532 nm experiment at ∼5 mJ cm-2 fluence, both the initial sample temperature and its dynamic evolution are well captured by a one-dimensional thermal energy deposition and diffusion model. The thermal conductivity k = (1.3 ± 0.4) W m-1 K-1 derived from this model is in good agreement with the literature value for CuO powder, kpowder = 1.013 W m-1 K-1. For 355 nm excitation, a quantitative analysis of the experiments is hampered by the large temperature gradients within the probed sample volume owing to the small UV penetration depth. The impact of the findings on mitigating or utilizing photoinduced lattice temperature changes in future X-ray free electron laser (XFEL) experiments is discussed.