Having seen 2 cars burn last year (one to the point of complete right off,) I can tell you that they don't explode like they do in films, and they take quite a while to get to that point. It takes a bit of faith to continue driving something that you can see flames actually coming out of, but in all reality you would have many clues that your car is not happy before then.
The first car I saw burn did explode. We were riding horses in a field, and someone had pulled into a byway to watch us riding. For reasons that never became clear, he parked practically on top of a fire that the farmer had lit which was still just about smouldering. After we had been riding for about 20 minutes, someone said 'is that car on fire?' and we gathered all the horses to the far end of the field as far away from it as we could and sat there to watch while one of the riders called 999. We watched for ages. The flames got a bit bigger, and eventually took over the car, but that took a good 10 minutes more. Another 5 minutes later, the car's fuel tank exploded. It was a muffled bang. The tires exploding were louder and more dramatic. The car remained where it was when bits of it were exploding, it didn't get thrown around by the force of any explosion. So from parking on a pile of embers to having the fuel tank explode was about 30 minutes in total.
The second car I saw burn had pulled up at a traffic lights with smoke coming out from under the bonnet. The driver opened the bonnet and smoke poured out followed by some small flames. I saw this (don't know how long he had been there) as I was driving the opposite way on a dual carriage way. As I had a fire extinguisher in my car I went up to the next turning point, did a U turn and drove back to the burning car and got my fire extinguisher out. We emptied the fire extinguisher into the flames which put them out, and then the driver carried on pouring bottled water which other drivers were handing him over the engine to cool it. I checked he was OK and then had to head off. By the time I had turned back onto the right direction for me on the dual carriage way and saw him again, he had managed to drive the car off the road so it was no longer blocking the junction and was waiting for a tow truck. It was not very dramatic.
The best piece of advice I can give here is to make sure you have a fire extinguisher in your car. I don't know why it's not a thing in this country. Its a legal requirement in many other countries in Europe.