I think it would be less than 55W because if the battery is at 12V, the charger is at 12.04V and the battery's internal resistance is 10 mOhm, you're only charging with a net voltage of 0.04 over 0.01 ohms so there's your 4A. If the voltages were equal you'd get no current flow so really the power dissipation would be 4^2 x 0.01 = 0.16W. Not sure how an amp works internally but if it's really consuming 120W, then my efficiency is even worse but I guess the bottom line is I don't care about that... at least in terms of consumption. I only care about the cooling implications and the chip is heatsinked. My "brick" power supply has the same exact op amp IC driving it and I've charged my car with that thing already. With a tiny little fan pointed at it, it actually performed admirably at 6A or so.