Ammonia inversion lines are often used as probes of the physical conditions in the dense interstellar medium. The excitation temperature between the first two para-metastable (rotational) levels is an excellent probe of the gas kinetic temperature. However, the calibration of this ammonia thermometer depends on the accuracy of the collisional rates with H2. Here, we present new collisional rates for ortho- and para-NH3 colliding with para-H2(J = 0), and investigate the effects of these new rates on the excitation of ammonia. Scattering calculations employ a new, high-accuracy, potential energy surface computed at the coupled-cluster CCSD(T) level with a basis set extrapolation procedure. Rates are obtained for all transitions involving ammonia levels with J <= 3 and for kinetic temperatures in the range 5-100 K. We find that the calibration curve of the ammonia thermometer - which relates the observed excitation temperature between the first two para-metastable levels to the gas kinetic temperature - does not change significantly when these new rates are used. Thus, the calibration of ammonia thermometer appears to be robust. Effects of the new rates on the excitation temperature of inversion and rotation-inversion transitions are also found to be small.