100 horsepower * 0.45 pounds of gasoline per horsepower-hour = 45 pounds of gasoline per hour
45 pounds of gasoline per hour * 1/3 of energy content to the radiator = 15 pounds of gasoline energy content to the radiator per hour
Gasoline requires 0.53 British Thermal Units to raise 1 pound of fuel by 1 degree Fahrenheit (
source). Gasoline contains 114,000 BTU of energy per gallon (
source), with a gallon of gasoline weighing 5.91 pounds or more (
source), giving an energy content of 19289.34 BTU per pound.
15 pounds of gasoline energy content to the radiator per hour * 19,289.34 BTU per gallon of gasoline = 289,340.1 BTU to the radiator per hour
72 degrees Fahrenheit seems like a good starting temperature for the fuel, which means the gasoline can't warm more than 118 degrees Fahrenheit before it starts warming the engine instead of cooling it.
I'm not sure how to continue from here. I'm not from an engineering background so I'm not sure of the equation to use going forwards. There's a formula for heating energy where I found the specific heat content for gasoline (
here), but it seems overly simplistic for this calculation. It's quite literally not taking place in a vacuum and some of the heat should be lost to the atmosphere through the radiator. After all, engines more powerful than this theoretical one have been cooled purely by air, with no liquid at all.