The definition of a brown dwarf is that there is enough heat and compression for deuterium and/or lithium fusion, but not protium fusion.

The exact model limit is unclear, but the physics modelling is relatively straightforward.

I had only the vaguest notion up until 15 minutes ago of how these are being categorized, this one is described as either a brown dwarf or giant planet? https://en.wikipedia.org/wiki/CoRoT-3b

see the Classification header of the page