  We give further support to Smirnov's conjecture on the exact kink S-matrix
for the massive Quantum Field Theory describing the integrable perturbation of
the c=0.7 minimal Conformal Field theory (known to describe the tri-critical
Ising model) by the operator $\phi_{2,1}$. This operator has conformal
dimensions $(7/16,7/16)$ and is identified with the subleading magnetic
operator of the tri-critical Ising model. In this paper we apply the
Thermodynamic Bethe Ansatz (TBA) approach to the kink scattering theory by
explicitly utilising its relationship with the solvable lattice hard hexagon
model. Analytically examining the ultraviolet scaling limit we recover the
expected central charge c=0.7 of the tri-critical Ising model. We also compare
numerical values for the ground state energy of the finite size system obtained
from the TBA equations with the results obtained by the Truncated Conformal
Space Approach and Conformal Perturbation Theory.
