The fraction of ionized gas in the warm-hot intergalactic medium induces temperature anisotropies on the cosmic microwave background similar to those of clusters of galaxies. The Sunyaev-Zel'dovich (SZ) anisotropies due to these low-density, weakly non-linear, baryon filaments cannot be distinguished from that of clusters using frequency information, but they can be separated since their angular scales are very different. To determine the relative contribution of the WHIM SZ signal to the radiation power spectrum of temperature anisotropies, we explore the parameter space of the concordance Λ cold dark matter model using Monte Carlo Markov chains and the Wilkinson Microwave Anisotropy Probe 7 yr and South Pole Telescope data. We find marginal evidence of a contribution by diffuse gas, with amplitudes of AWHIM = 10-20 μK2, but the results are also compatible with a null contribution from the WHIM, allowing us to set an upper limit of AWHIM < 43 μK2 (95.4 per cent CL). The signal produced by galaxy clusters remains at ACL = 4.5 μK2, a value similar to what is obtained when no WHIM is included. From the measured WHIM amplitude, we constrain the temperature-density phase diagram of the diffuse gas, and find it to be compatible with numerical simulations. The corresponding baryon fraction in the WHIM varies from 0.43 to 0.47, depending on model parameters. The forthcoming Planck data could set tighter constraints on the temperature-density relation.