This phenomenon -whereby the inside of a car gets really very hot, much hotter than the outside -is known as the GREENHOUSE effect.

This is what happens. Sun light travels from the sun in the visible part of the spectrum (i.e. we can see it!) and strikes the inside surface of the car. The sunlight is absorbed by the surface of the car (say the dashboard and the carpet) and since radiation is energy, the absorption of the visible radiation causes the surface that is struck to heat up. Now---- and this is the key part---- EVERY OBJECT emits energy at a wave length that is a function of the temperature of the object. Human beings around 100 deg F emit radiation in the INFRARED part of the spectrum. The human EYE cannot see this emitted radiation unless one uses special Goggles that enable this radiation to be converted to a range that the eye CAN see. In fact, this principle is the basis for NIGHT VISION goggles. Also SNAKES that catch rodents in the desert at night have such IR heat sensors!!!...

At any rate, sunlight falls on the carpet of your car and then the carpet RE RADIATES that, the absorbed visible (short wave length) energy in the IR (long wave length) part of the spectrum. BUT water vapor and CO₂ in the air in your car will ABSORB this re-radiated IR energy (the water and CO₂ is transparent to the incoming visible radiation) and so the heat gets trapped in your car. This is because the incoming visible light gets absorbed and re-radiated at longer wave lengths and these long wave lengths are TRAPPED by the small amount of water vapor and CO₂ present in the car.

NEVER EVER leave a PET or a small child in such a situation... even if the temp outside is say 70 deg F which is not so hot, the interior of a car can easily exceed 100 deg F.

Green house effect! The air inside heats up, but the car is sealed and there is no where for the air to escape.

The car is heated by sunshine. Actually, everything is heated by sunshine, but things outside the car are cooled off by the outside air, since the air is cooler than they are. Inside the car, the air is trapped, so it heats up to the same temperature as the car.

Radiation from the Sun is absorbed, through the glass, by the inside of the car. That is why it helps to a) have tinted glass or b) use a screen on the windows while it is parked.