Thermal response factors to a 2nd order shaping function for the calculation of the 1D heat conduction in a multi-layered slab

•First implementation of the thermal response factor method using 2nd order holder.•First implementation which shows the use of thermal response factors with more than one parameter.•Stimulate new research or modification of the present methods.•Recalls the attention about how to employ new shaping functions to achieve a energy-conservative, stable and accurate method for heat transfer.•Shows that it is capable of computing at 1h step reaching an accuracy equivalent to the 5min step of the traditional Mitalas’ method.