Welcome to Fluther.
What’s wrong with radiation?
If you’ve ever visited a hibachi restaurant you can often feel the radiated heat from when they light off the hibachi several tables away (or even a full room away) nearly instantaneously.
Other than that I would say “generally conduction”, although it matters greatly what the conductor is. If you light a fire in a fireproof safe, for example, you’ll feel the heat at the open door (convection) far sooner than you would through the conduction of the metal sides, since they’re insulated to protect against the heat. Materials matter. Also, if there are air / flue gas currents set up, the convective heat along that stream can travel as quickly as the convective media, too.
Setup matters. Materials matter.