We present a novel approach for reconstructing the Holocene surface temperature histories by forcing the output of a firn densification and heat diffusion model to fit nitrogen isotope data (δ<sup>15</sup>N) extracted from ancient air in Greenland ice cores. The performance of this novel approach is demonstrated using synthetic data. The presented approach works completely automated and leads to a match of the δ<sup>15</sup>N target data in the low permeg level and to related temperature deviations of a few tenths of Kelvin for different data scenarios, showing the robustness of the reconstruction method. The obtained, final mismatches follow a symmetric, standard distribution function. 95% of the mismatches compared to the synthetic target data are in an envelope in between 3.0-6.3 permeg for δ<sup>15</sup>N and 0.23-0.51 K for temperature (2σ, respectively). We solve the inverse problem T(δ<sup>15</sup>N) by using a combination of Monte Carlo sampling and quantitative data analysis, based on cubic spline filtering of random numbers and the measured temperature sensitivity for nitrogen isotopes. Additionally, the presented reconstruction approach was tested by fitting δ<sup>40</sup>Ar and δ<sup>15</sup>N<sub>excess</sub> data (Döring et al., in prep.), which leads to same robust agreement between modelled and measurement data. In addition to Holocene temperature reconstructions, the fitting approach can also be used for glacial temperature reconstructions (Döring et al., in prep.) and it is reasonable to adapt the approach for model inversions of other non-linear physical processes.