That is true, I wasn't sure whether to suggest modeling up the thermal capacitance of the jacket. The problem there is that several other factors need to be characterized:
The actual right answer would require a model inclusive of the above. Assuming the jacket is reasonably insulative and has a somewhat low thermal mass (befitting modern fabrics and design) then jacket inner surface vs. ambient air is a reasonable simplification. If the jacket is an older-school, thick cotton or leather get-up e.g. it has a lot of thermal mass then the answer will depend a great deal on the above factors.
- The thermal connection between the jacket, the individual's clothing and their skin all of which will have [likely] very different Rths
- The degree to which the jacket actually was cold-soaked e.g. delta T between inner and outer surface, and what the thermal gradient looks like
- Definition of what the "warm room" actually means from a thermal point of view e.g. are there radiative heat sources in the vicinity or are we talking warm, still air or are we talking warm air and decent convection
Wow, Phoenix! It sounds like you really know this stuff! Thanks for that analysis!