In my opinion a Peltier cooler is not an option due to the excessive power required.
Rather than a fan, is it possible to rely on the fact that the car is moving through the aire anyway?
I imagine that using the car's chassis as a heatsink is probably the best option. You could probably dump quite a lot of heat into the chassis and hardly get any temperature rise at all.
How are you gong to power the LED?
I wouldn't recommend a resistor due to the excessive power dissipation. High power LEDs also often have quite a high voltage drop because they're actually composed of many smaller LEDs connected in series and parallel. For both reasons you really need a switched mode constant current power supply.
As far as monitoring the temperature is concerned, I've noticed that the forward voltage drops with temperature which might in itself help guard against overheating if a constant current supply is used, if not you could cut the power if the voltage drop is too low.
Usable lamp life is something you need to consider because LEDs get dimmer with age. I'd recommend underrating the LED slightly because not only does it make LEDs last longer, they're also more efficient at lower currents: running at 80% of the current rating does not normally reduce the brightness to 80% of the full rating, it's normally closer to 90%, see the datasheet to be sure.