First, you would need a HOT heat source under the console to cook off a round. There is simply not one there inside the car, period. The exhaust system is the only thing hot enough to do it, and it is of course, on the outside of the car, closer to the tank full of gasoline than a round dropped in the car would ever get.
Second, if it did cook off (not really possible), being outside a chamber, as someone mentioned the case would go further than the bullet since it is lighter. Pressure would be released the second the bullet and case separate, i.e., no chamber and no barrel = no pressure = no velocity.
If you somehow managed to put a several hundred degree heat source under there to generate a cook off, the only slight danger would be from something under there flammable enough to catch fire in the second or two it would take for the few grains of powder to burn to completion. Any heat source hot enough to cook off a round is likely hot enough to combust any easy combustible material under there.
We can all appreciate trying to keep our family safe, but properly evaluating risk helps rather than hurts our effort on that topic; I'm sure we'd all agree. A loose round under the seat does not represent a risk. There are plenty of activities we do every day that are relatively risky, and reasonable things we can do to mitigate those risks... this just doesn't fall in that category.