Heat transfer measurements are required in a wide range of fields, for example to validate new cooling concepts in turbomachinery, to assess the performances of heat exchangers, and to provide data for numerical simulations. Thereby transient methods are often applied for local heat transfer resolution. A particular challenge is posed by complex flows, where the determination of the heat transfer coefficients with the commonly applied transient heater mesh method can prove difficult, for instance in cases in which the flow can take different paths leading to mixing flows at different temperatures, and a difficult determination of the reference temperature. One way to address these complex systems is the transient heater foil method, in which the experiment is driven by a constant heat flux generated at the surface under study, instead of a temperature variation in the flow. However, the accuracy of the measurement remains an open issue compared to the heater mesh method. Here we show a modification of the heater foil method, which uses a linearly increasing surface heat flux to improve the measurement accuracy, especially in the low heat transfer regions. The new method is validated by measuring the heat transfer of a single circular jet perpendicularly impinging on a flat plate, and by comparing the results to a correlation available in the literature. Results show good agreement with the literature, while providing considerable accuracy improvement with respect to the heater foil method with constant heat flux. The heater foil method presented here, reaches similar uncertainty values as the state of the art versions of the heater mesh method in low heat transfer regions, while providing better accuracy in the high heat transfer regions. Additionally, it allows for an easier implementation for certain problems, provided that optical access is guaranteed and the surface curvature allows for the addition of the heater foil.