also when you wire up your amps to a 2 ohm load as opposed to a 4 ohm load the power cycles faster through the amp ( which is why it is capable of the higher power rating ) but that also will cause your amp to generate more heat. This overheating can destroy your amp if not controlled

Your conclusion is correct- more heat is produced in a 2 ohm system vs a 4 ohm system

your explanation as to why it is warmer was not correct- 1) changing the ohm load does not change the speed of electricity (cycles faster), 2) a faster amp should not generate more power or more heat than an amp with a slower rise 3) heat in a speaker is a function of current flow, a lower resistance produces more current flow 4) heat in an amplifier is a function of current produced and efficiency