Most riding lawn mowers do not have any radiators and instead are air cooled engines.
However some high end more expensive models of riding lawn mowers do have radiators that use coolant and the radiator to dissipate heat.
Most lower end riding motors use air to cool the engines by using metal fins on the engine heads to move the heat away from the engine.
Air cooled engines don't cool as good as liquid cooled engines but they cool enough to keep the engine from overheating.
The amount of fuel that a lawn mower uses per hour depends on the lawn mower and the size of the engine.
Most riding lawn mowers use around 1.65 gallons of gasoline per hour.
Most diesel lawn mowers use around 1 gallon of diesel per hour.
The lower the engine RPM the less fuel it will use and the higher the RPM the more fuel the lawn mower will use.
A push lawn mower often uses a 1/2 gallon of fuel for an hour of run time.
Riding mowers have larger engines and the higher you have the throttle the more gasoline it will consume.
Also if you're cutting tall grass the lawn mower engine will often use some more fuel to power through the grass.
Some larger zero turn mowers can use up to 2 gallons of gasoline per hour.
An average riding mower holds around 1 to 2 gallons of gas although larger riding mowers may hold up to 5 to 6 gallons of gas.