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 in a semi-continuous or pulsed manner at one or more locations 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 time of flight model is used to determine, for a plurality of points of interest, a fluid flow direction, bulk flow rate and/or a cumulative flow rate contribution.