A thermally controlled stage is connected within one arm of a bridge of a capillary bridge viscometer so that the bridge can be balanced in situ to provide accurate measurement signals. The thermally controlled stage includes a tuning capillary tubing portion that is wrapped around a thermally conductive core. A resistance heater or a Peltier thermoelectric device is located in close proximity to the capillary tubing portion. The heater or Peltier device and the capillary tubing portion are located within a thermally insulated housing. The heater or Peltier device varies the temperature of the capillary tubing portion to cause a corresponding change in the flow impedance of the tuning capillary tubing portion of the arm of the bridge in which the thermally controlled stage is connected. The temperature of the tuning capillary tubing portion is monitored and adjusted until any pressure differential across the bridge is eliminated, whereby to trim in the balance of the bridge.