We investigate the viability of the quasi-temporal gauge on the lattice. This is a complete gauge fixing condition that can be implemented on the lattice at a very low computational cost. As a test case, using the Clover action, we have evaluated the (gauge invariant) renormalisation constant of the non-singlet axial current, using Ward identities extracted from quark states. Our result is in reasonable but not complete agreement with previous values obtained from Ward identities both on hadronic states and on quark states in the Landau gauge. We observe large fluctuations due to lattice Gribov copies. The influence of finite volume effects is expected to be non-negligible in the case we are considering.