There are models but are specific to tree specie . Fire intensity, bark thickness or dbh instead are used as input variables but they should be adjusted to each specie because bark heat conductivity could be different. Logistic models are usually used.

There is a very good introductory discussion of the relationship between bark characteristics and tree mortality, in the context of western North American conifer trees, in Agee's classic textbook Fire Ecology of Pacific Northwest Forests (1993: p. 118-124). Older work is cited based on thermal diffusivity, while more practically-oriented models consist of empirical relationships based on species, temperature, and critical time for cambial kill. For example, at a fire temperature of 500 degrees C, Peterson and Ryan (Environmental Management 10: 797-808 (1986)) found the relationship t=2.9x2, where t is time to cambial kill and x is bark thickness in cm.

For more recent (and much more complex) models at the levels of plume physics and cellular necrosis, see the work of S. Michaletz, for instance Michaletz and Johnson (Canadian J. of Forest Research 38: 2013-2029 (2008)).

As damage caused by forest fire is inversely related to dbh of any particular tree, smaller is the dbh more is the damage and more will be stem damage eventually. 

Damage also depends on environmental factors such as wind velocity, weather conditions, humidity, temperature etc. Considering all these variables in mind, a model predicting stem damage in response in to forest fire can be built.