The effective viscosity of helium in the transition regime has been measured at different external thermal gradients with a rotatory cylinder viscometer used as a damped oscillator. It was found that the viscosity of helium does not vary monotonically with the gradient of temperature, showing an appreciable change at G = 6.9 +/- 0.8 K/cm for average temperatures between 293 and 327 K and a distance between the fixed and moving plates of 2.0 +/- 0.1 cm. Similar experiments held at constant thermal gradients and variable pressure indicated that under those conditions, and within the range 1-150 mu mHg, the viscosity of helium presents two regions of rapid variation with the pressure whose positions depend on the magnitude of the thermal gradient. Some general characteristics of the behavior found can be predicted in terms of a simple theory based on the Boltzmann equation under the relaxation time approximation, although the detailed variation of the shear viscosity with the thermal gradients awaits a thorough explaination. It is clear, however, that higher order terms in the collision time are required for the theoretical consideration of this effect. The region of rapid variation of the shear viscosity at constant thermal gradient and varying pressure can be theoretically reproduced assuming a molecular diameter for helium of 3.1 +/- 0.3 Angstrom, while those at constant pressure and variable thermal gradient can be reproduced for a diameter of 1.9 +/- 0.3 Angstrom. The first of these values is close to the currently accepted diameter of helium gas deduced from theoretical computations and van der Waals excluded volume measurements. On the other hand, the second value is close to the shear viscosity and thermal conductivity measurements in the continuous regime.