This thesis studies how past ground surface temperatures can be reconstructed from temperature measurements in permafrost boreholes. Such reconstructions are important because direct observations usually cover only the last few decades, while boreholes can preserve information about much longer-term ground warming and cooling. However, this is a difficult inverse problem: small errors in the measurements, uncertainty in soil properties, and simplified model assumptions can strongly affect the final reconstruction. The work builds on an existing Bayesian inversion method based on Ensemble Kalman Sampling (EKS). The main extension proposed in this thesis is a multiple-likelihood framework. Instead of using only one temperature-depth profile from a borehole, the method can combine several profiles measured at different times at the same site, including non-consecutive years. In addition, the thesis introduces a data-driven prior for ground surface temperature histories. This prior is derived from observed or reanalysis-based air temperature data and transformed with an n-factor approach to better represent the coupling between air and ground temperatures. The method is tested on three permafrost borehole sites in the Lena River Delta region: Sardakh, Samoylov, and Tiksi. A systematic sensitivity analysis is carried out to examine how the results depend on measurement noise, the number and timing of the selected borehole profiles, and borehole depth. The study also investigates how far back in time useful climate information can be recovered from shallow and deeper boreholes. The results show that the combination of multiple likelihoods and the data-driven ERA-based prior improves the reconstruction mainly by slightly reducing posterior uncertainty and by producing more physically plausible temperature histories. In particular, the Pearson correlation indicates that these methodological extensions help to reconstruct the temporal pattern of ground surface temperature more accurately, meaning that warming and cooling phases are captured more consistently over time. However, the RMSE results also show that for low or realistic noise scale settings, the reconstruction error can increase instead of decrease. This suggests that the main value of the proposed method lies in better recovery of the temporal structure and improved interpretability, rather than in a systematic improvement of absolute numerical accuracy. Overall, the thesis demonstrates that repeated borehole measurements can help the inversion framework reconstruct temporal patterns more robustly. Although the method cannot overcome the physical limits imposed by thermal diffusion or simplified forward models, it provides a practical and more reliable framework for reconstructing historical ground surface temperatures from existing permafrost borehole datasets.