The total cross section for the production of massive quarks in electron
positron annihilation can be predicted in perturbative QCD. After
expansion in m^2/s the quartic terms, i.e. those proportional to
m^4/s^2, are calculated up to order \alpha_s^3 for vector and axial
current induced rates. Predictions relevant for charm, bottom and top
quarks production are presented. The \alpha_s^3 corrections are shown to
be comparable to terms of order \alpha_s and \alpha_s^2. As a
consequence, the predictions exhibit a sizeable dependence on the
renormalization scale. The stability of the prediction is improved and,
at the same time, the relative size of the large order terms decreases
by replacing the running mass \bar{m}(\mu) with the scheme independent
invariant one \hat{m}. By combining these results with the prediction
for massless case and the quadratic mass terms the cross section for
massive quark production at electron positron colliders is put under
control in order \alpha_s^3 from the high energy region down to fairly
low energies.