  We consider a finite element method with symmetric stabilisation for the
discretisation of the transient convection--diffusion equation. For the
time-discretisation we consider either the second order backwards
differentiation formula or the Crank-Nicolson method. Both the convection term
and the associated stabilisation are treated explicitly using an extrapolated
approximate solution. We prove stability of the method and the $\tau^2 +
h^{p+{\frac12}}$ error estimates for the $L^2$-norm under either the standard
hyperbolic CFL condition, when piecewise affine ($p=1$) approximation is used,
or in the case of finite element approximation of order $p \ge 1$, a stronger,
so-called $4/3$-CFL, i.e. $\tau \leq C h^{4/3}$. The theory is illustrated with
some numerical examples.
