The heat pulse method for the measurement of the rate of sap flow in plants suffers from two drawbacks, viz. the discontinuous nature of the measurements and the lack of a precise mathematical formulation of the heat fluxes. To overcome these drawbacks a random noise heat signal has been used as an input and two sensor pairs have been used for the measurement. A model is given that employs the signal from one sensor pair as input and the signal from the second pair as output of a heat transport system. Thus the adverse effects of radial heat conduction have been eliminated. Simulation models with the rate of sap flow as one of the parameters have been fitted to the stationary response data with an on-line parameter optimization algorithm. The method has been validated in applications to artificial data and to real data obtained from a plastic tube and from tomato plants.