Will putting a light bulb under the hood in cold weather help the car start better?

That depends. Back in the 70s my dad had a car that wouldn't start unless he did. I have a Ford Explorer that can be troublesome to start when the temps drop into the teens and below; a heat lamp under the hood helps. Does the car turn over fine but won't start? Or is the problem with the battery meaning that the car just won't crank fast enough for the car to start? (The problem I have relates to fuel combustion, not battery cranking power.)

Other factors can cause difficulty in cold weather starting. If fuel related, use a winter gas treatment with each tank of gas. A car that's in a poor state of tune can also fail to start in cold weather, even if it seemed to run fine during warmer temps. If the battery just wont crank, you can try leaving it on a trickle charger overnight or have your charging system tested.

As for the light bulb, try it. If it helps your car start at certain temps, do it. If not, you may need to look at other options such as an engine block or coolant heater.

A couple of safety precautions: 1) Be sure that you place the bulb under the hood where it won't be too close to rubber or non-metal components that could be damaged or start a fire; 2) Be careful with electrical cords in the wet and snow (best to use a grounded cords); 3) Route the cords so that they won't be sucked into the fan or belts if you should start your engine before removing them; 4) Consider putting something on the steering wheel, like a red string, to remind you that the car is plugged in so that you don't drive away by accident while the cords are plugged in.