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Model parameters are among the primary sources of uncertainties in land surface models (LSMs). Over the Tibetan Plateau (TP), simulations of land surface processes, which have not been well captured by current LSMs, can significantly affect the accurate representations of the weather and climate impacts of the TP in numerical weather prediction and climate models. Therefore, to provide guidelines for improving the performance of LSMs over the TP, it is essential to quantify the uncertainties in the simulated land surface processes associated with model parameters and detect the most sensitive parameters. In this study, five observational sites were selected to well represent the land surfaces of the entire TP. The impacts of 28 uncertain parameters from the common land model (CoLM) on the simulated surface heat fluxes (including sensible and latent heat fluxes) and soil temperature were quantified using the approach of conditional nonlinear optimal perturbation related to parameters (CNOP-P). The results showed that parametric uncertainties could induce considerable simulation uncertainties in surface heat fluxes and soil temperature. Thus, errors in parameters should be reduced. To inform future parameter estimation efforts, a three-step sensitivity analysis framework based on the CNOP-P was applied to identify the most sensitive parameter combinations with four member parameters for sensible and latent heat fluxes as well as soil temperature. Additionally, the most sensitive parameter combinations were screened out and showed variations with the target state variables and sites. However, the combinations also bore some similarities. Generally, three or four members from the most sensitive combinations were soil texture related. Furthermore, it was only at the wetter sites that parameters related to vegetation were contained in the most sensitive parameter combinations. In the future, studies on parameter estimations through multiobjective or single-objective optimization can be conducted to improve the performance of LSMs over the TP.