Experimental heat transfer measurements are used 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. A particular challenge is posed by complex geometries, where the heat transfer coefficients cannot be determined with the usual transient heater mesh method. One way to address these complex systems is the transient heater foil method, which generates a constant heat flux in the metal foil, which is attached at the surface to be measured. 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 heat flux in the foil to improve the measurement accuracy, especially in low heat transfer regions. The new method is presented using a single impingement cooling setup; results demonstrate good agreement with the baseline method (heater foil with step heating) and the literature, while the accuracy is improved.