Mineralogical transformations and material transfers within the Earth's mantle make the 350–1000 km depth range (referred here as the mantle transition zone) highly heterogeneous and anisotropic. Most of the 3-D global tomographic models are anchored on small perturbations from 1-D models such as PREM, and are secondly interpreted in terms of temperature and composition distributions. However, the degree of heterogeneity in the transition zone can be strong enough so that the concept of a 1-D reference seismic model must be addressed. To avoid the use of any seismic reference model, we present in this paper a Markov chain Monte Carlo algorithm to directly interpret surface wave dispersion curves in terms of temperature and radial anisotropy distributions, here considering a given composition of the mantle. These interpretations are based on laboratory measurements of elastic moduli and Birch–Murnaghan equation of state. An originality of the algorithm is its ability to explore both smoothly varying models and first-order discontinuities, using C1-Bézier curves, which interpolate the randomly chosen values for depth, temperature and radial anisotropy. This parametrization is able to generate a self-adapting parameter space exploration while reducing the computing time. Thanks to a Bayesian exploration, the probability distributions on temperature and anisotropy are governed by uncertainties on the data set. The method is applied to both synthetic data and real dispersion curves. Though surface wave data are weakly sensitive to the sharpness of the of the mid-mantle seismic discontinuities, the interpretation of the temperature distribution is highly related to the chosen composition and to the modelling of mineralogical phase transformations. Surface wave measurements along the Vanuatu–California path suggest a strong anisotropy above 400 km depth, which decreases below, and a monotonous temperature distribution between 350 and 1000 km depth.