There was a low-speed collision with a deer (approximately 10-15 mph). The vehicle continued to run fine after the collision and we were able to drive it home. After the next start, the engine was shaking all over and started smoking from behind the engine. The battery was disconnected but it continued to smoke. After further inspection, we were able to find a fire and extinguished it using a fire extinguisher. We had issues with this car prior to the collision where the engine would misfire after the car would get wet, but would only produce temporary codes. This was checked out by the dealer and we were told there's nothing that they can do. A few weeks prior to the collision it happened again and the check engine light went to a confirmed/permanent code and it was related to cylinder misfires. If we would not have had a fire extinguisher or had been able to roll it away from the house, the occupants, vehicle, and house would have been in danger of the fire. The source of the ignition has been confirmed to be the ignition coils, but the root cause of this has not been determined and it has just been assumed that it is related to the collision, without an actual root cause identification.