New path integral Monte Carlo constant volume specific heat (C-V) estimators are presented that improve upon the thermodynamic, virial, and centroid virial C-V estimators via a free particle projection. These projected estimators significantly reduce the numerical noise of the traditional estimators. The new projected thermodynamic estimator has particular advantages when derivatives of the potential are expensive to evaluate. A double virial estimator is derived for real space path integrals and comparisons are made to it. The centroid virial estimators are found to be significantly better than the noncentroid virial estimators.