Provided is a compact apparatus for measuring the flow rate of a fluid. The apparatus includes a heated measure element and a heated reference element which are in substantially the same thermal environment within a measure cell, except that the measure element is situated in the path of the cooling fluid flow and the reference element is sheltered from this direct fluid flow. These elements are arranged as parallel and concentric planar elements that are essentially identical to each other with matching thermal characteristics. The elements are electrically connected in a Wheatstone bridge arrangement. Thermal exchange between the reference and measure elements is used to optimise noise rejection due to common mode background thermal effects. Measured parameters from the bridge can be used to derive the fluid flow rate.