Second order ${\cal O}(\alpha_s^2)$ corrections to the heavy quark
production cross-section due to massless quarks and coloured scalars
are calculated for all energies above threshold. Based on the method
introduced in this letter also the gauge non-invariant second order
corrections due to the pure gluonic self-energy insertion and a certain
class of ${\cal{O}}(\alpha_s^3)$ and
${\cal{O}}(\alpha_s^4)$ corrections are
determined. For the special choice of the gauge parameter, $\xi=4$, the
leading threshold and high energy behaviour of the pure second order
gluonic corrections to the cross-section are governed by the
gluonic self-energy insertion.