A key input component of numerous reliability studies of industrial components or structures, steel fracture toughness is usually considered as a random process because of its natural variability. Moreover, toughness presents a high sensitivity to temperature which also plays a fundamental role, as an environmental forcing, in such studies. Therefore a particular attention has to be paid to the assessment of its stochastic functional modelling, by means of a statistical analysis of indirect measures that suffer from heterogeneity and censoring. While a Weibull shape arising from statistical physics is recognized as the most relevant approach to represent local variability, the selection of best functional parameters (function of temperature) requires an accurate estimation and testing methodology. Its development is motivated by several limitations of the common statistical practices in the field of fracture toughness, which are related to data treatment and model selection. Illustrated by the exploration of a database feed by several European manufacturers or exploiters, this article establishes the main steps of such a methodology, implemented in a dedicated software tool.