A system of thermodynamic Bethe ansatz equations is suggested for integrable perturbation of the Z N parafermion CFT model by the basic parafermion field. Several checks are performed to justify the relevance of the system suggested. In the limit N→∞ we obtain an infinite TBA system describing the finite size effects in the non-linear O(3) sigma model. Certain modified Z z parafermion perturbations are introduced, which are argued to converge at N→∞ to the O(3) sigma model with the θ term. For θ= π we suggest for every N a massless TBA system describing the interpolating renormalizaition group flow from the ultraviolet Z N fixed point to the infrared fixed point, which turns out to be the minimal unitary CFT model MN+1.