If you will, it’s not that simple. Rising temperatures can be both a cause and a result of climate warming. Also, it might be a result of increased volcanism. Personally I feel that the key triggers are plate tectonics and most importantly solar output. However the man lesson seems to be that you can’t look at one thing in isolation. I haven’t even mentioned ocean currents and the are influential.
Ocean currents are actually very important, as you state. The flow or flux of energy is far more important then temperature readings. Especially atmospheric temperatures which represent very minor proportions of the total energy flux. Apes holding thermometers have no clue what they are doing. If there was no water current and all Oceans were stagnant, the equatorial surface layers would be very warm and the deeper and polar regions very cold. Basically a constant El Nino. Solar energy fluxing from ocean surface to atmosphere.