Most railguns I've read about produce extreme g-loads. Most people would come out as super-gross wonder-jelly if fired out of one. I think what you want is some kind of electromagnetic accelerator, but not necessarily a railgun in particular.
> On its own that space would heat up due to the friction on the gas, but you can put a heat sink (eg a block of ice) in the car and keep it comfortable inside.
The cabin of a vehicle is quite small, and the ride time is quite short, so a large block of ice probably would be feasible. But you are talking about having a car leave every second, so for each loop you would have to have a plant capable of freezing something like 2 gallons of water per second, as well as a means of refilling the ice container in each car. That's going to add quite a bit to the expense and energy use of the system you describe. Refrigeration systems become quite a bit more efficient as they become larger, so probably this is manageable.
Depending on how quickly you can turn around each car, each loop might require quite a few additional cars. (But still a fraction of the total number)