If the viscosity can be expressed in the form rl = a ( T ) f ( a ) , the walls are at a constant temperature To, and the extra stress, velocity and temperature fields are fully developed, then the wall shear rate ~)w can be calculated by applying the Weissenberg-Rabinowitsch operator to F~Q instead of to the flow rate Q, where Fc is a correction factor which differs from 1 when the temperature field is non-uniform; the isothermal equation relating the wall shear stress and pressure gradient is still valid. For the case in whcih ~7 = ~0lal n/(1 + fl(T-To)), where n, ~/0, and fl are independent of shear stress a and temperature T, an exact analytical expression for F c in terms of the NahmeGriffith number N a and n is obtained. Use of this expression gives agreement with data obtained for degassed decalin (r/= 2.5 mPa s) from a new miniature slit-die viscometer at shear rates # up to 5× 10 6 S-l; here, the correction is only 7070, Na is 1.3, and Gz, the Graetz number at the die exit, is 119. For a Cannon standard liquid $6 (~/=9mPas), agreement extends up to 5×105s-1; at 2× 106 s -~ (where Na = 7.2 and Gz = 231), the corrections are 1107o (measured) and 3607o (calculated).