A method and apparatus are provided for determining movement of a fluid into or out of a subsurface wellbore, to thereby enable accurate allocation of fluids being produced by or injected into each of several zones of the wellbore. A temperature change is effected in the fluid at a first location in the wellbore. A temperature of the fluid is measured at one or more sensing locations downstream of the location of the temperature change. A simulated heat flow profile is generated from a wellbore model. The simulated heat flow profile is compared to the measured temperature of the fluid at the one or more sensing locations. An inversion model is used to determine, for a plurality of points of interest, a fluid flow direction and/or a cumulative flow rate contribution.