We have found a branching dependence of critical extrusion temperature in metallocene-catalysed linear and branched polyethylene, below which the commonly found surface distortion instabilities disappear. The elimination of these extrusion instabilities has been observed in a wide range of temperatures up to 23degreesC above the melting point of each polymer. However, in contrast to previous observations, a window of minimum flow resistance, i.e., extrusion pressure, is not detected. This low temperature effect is discussed in terms of a flow ordered phase at the wall that induces local chain orientation. This so-called mesophase would prevent the mechanism for the formation of distortions to operate below a critical temperature.