It might get up to 120-130F in the shaded parts inside the car on a sunny day. That is about 54C - which is well within the operating temperature range of the LED. In direct sunlight in the car (like on the dash), the light will get hotter, so avoid having it directly exposed to sunlight if you can.
There is one big risk to consider - if the focusing lens (either part of the LED package in 5mm LEDs, or a collimator for power LEDs) or reflector get pointed directly at the sun, that could easily destroy the LED in short order.
Remember, the optics of the flashlight are designed to redirect the light from a small, omnidirectional source (LED or bulb) into a parallel beam (which happens to be many times larger in diameter than the emitting surface of the LED chip its self). However, this also works in reverse. So you shine parallel beams of light into the optic/reflector (in this case, sunlight), and it will focus it into a tight spot right on the LED chip. Sunlight has a ton of energy (both visible and IR), so in that case, the little LED chip is now the perverbial ant being fryed by the magnifying glass.
Let's consider the case where you have a 1" reflector on a Luxeon III LED. The Luxeon III chip is 1mm^2. The 1" reflector has a surface area of 500 square millimeters. If you point that directly at the sun, suddenly the Luxeon chip is being exposed to 500x as much light/heat from the sun as it was before! In that circumstance, I probably wouldn't take much to destroy some part of the LED.
So, to sum up:
In the car in the shade - likely okay
In the car exposed to sunlight - probably not good
Pointed at the sun (ever) - BAD!