We extend our MCMC sampler of 3D EoR simulations, 21CMMC, to perform parameter estimation directly on light-cones of the cosmic 21cm signal. This brings theoretical analysis one step closer to matching the expected 21-cm signal from next generation interferometers like HERA and the SKA. Using the light-cone version of 21CMMC, we quantify biases in the recovered astrophysical parameters obtained from the 21cm power spectrum when using the co-eval approximation to fit a mock 3D light-cone observation. While ignoring the light-cone effect does not bias the parameters under most assumptions, it can still underestimate their uncertainties. However, significant biases (∼few – 10 σ) are possible if all of the following conditions are met: (i) foreground removal is very efficient, allowing large physical scales (k ∼ 0.1 Mpc−1) to be used in the analysis; (ii) theoretical modelling is accurate to ∼10 per cent in the power spectrum amplitude; and (iii) the 21cm signal evolves rapidly (i.e. the epochs of reionisation and heating overlap significantly