For a given type of bean, do different brewing processes and temperatures (drip, French press, Mocha, espresso, cold brew, etc.) produce coffee with different caffeine content?
It would seem temperature isn't a factor because, according to this answer, "caffeine is chemically stable even when passed through its boiling point (evaporation temperature) of 312°C (593.6°F)".
The brewing method, however, would seem to matter. Mocha, espresso machines would seem to extract the most caffeine because they require finer grounds and use higher temperatures (steam) and pressure.