Imposing a thermal and compositional significance to the outcome of the inversion of seismic data facilitates their interpretation. Using long-period seismic waveforms and an inversion approach that includes constraints from mineral physics, we find that lateral variations of temperature can explain a large part of the data in the upper mantle. The additional compositional signature of cratons emerges in the global model as well. Above 300 km, we obtain seismic geotherms that span the range of expected temperatures in various tectonic regions. Absolute velocities and gradients with depth are well constrained by the seismic data throughout the upper mantle, except near discontinuities. The seismic data are consistent with a slower transition zone and an overall faster shallow upper mantle, which is not compatible with a homogenous dry pyrolite composition. A gradual enrichment with depth in a garnet-rich component helps to reduce the observed discrepancies. A hydrated transition zone would help to lower the velocities in the transition zone, but it does not explain the seismic structure above it.