We present an application of the reaction class transition state theory (RC-TST) in predicting thermal rate constants of the hydrogen abstraction reactions H + H-C(sp(3)) where C(sp(3)) is a saturated carbon atom. Combining the RC-TST with the linear energy relationship (LER) allows rate constants of any reaction in the class to be estimated from only reaction energy information. We have derived from first-principles all parameters for the RC-TST/LER method so rate constants for any reaction in this class can be predicted from only reaction energy, that can easily be computed from either the density functional theory or semiempirical molecular orbital theory. We have performed error analyses for a large number of reactions in the above class for which some experimental measurements or estimates are available. By comparisons with results from full TST/Eckart calculations we also found the RC-TST/LER method is quite cost-effective and has accuracy comparable to first-principles predictions using more rigorous methodologies.