Philosophers argue that many choices in science are influenced by values or have value-implications, ranging from the preference for some research method's qualities to ethical estimation of the consequences of error. Based on the argument that awareness of values in the scientific process is a necessary first step to both avoid bias and attune science best to the needs of society, an analysis of the role of values in the physical climate science production process is provided. Model-based assessment of climate sensitivity is taken as an illustrative example; climate sensitivity is useful here because of its key role in climate science and relevance for policy, by having been the subject of several assessments over the past decades including a recent shift in assessment method, and because it enables insights that apply to numerous other aspects of climate science. It is found that value-judgements are relevant at every step of the model-based assessment process, with a differentiated role of non-epistemic values across the steps, impacting the assessment in various ways. Scrutiny of current philosophical norms for value-management highlights the need for those norms to be re-worked for broader applicability to climate science. Recent development in climate science turning away from direct use of models for climate sensitivity assessment also gives the opportunity to start investigating the role of values in alternative assessment methods, highlighting similarities and differences in terms of the role of values that encourage further study.