It sounds odd, but sometimes you can overheat an engine and do lots of damage, but the engine will still run. The problem is that more and more damage can be accumulating during this process, to the point where it then won’t run at all. Perhaps that’s what’s happened here.

Overheating can cause mayhem under the bonnet and you really need to have the engine assessed to see if its fixable or junk. Damage associated with overheating can include a blown head gasket, warped cylinder head, damaged piston rings and even complete engine seizure (although that’s clearly not the case with yours).

If the engine is toast, perhaps a tested second-hand replacement engine from a wrecked Barina might be the most financially appealing solution.

I’m not sure about other markets around the world, but the Barina Spark sold in Australia between 2010 and 2015 was a five-door hatchback. That is; it had four doors and a lift-up tailgate (hatchback) that is considered the fifth door.

At first glance, you might be forgiven for thinking that the Spark is, in fact, a three-door car, but that’s because the South Korean designers (the car is actually a Daewoo with Holden badges) styled it to look that way by hiding the rear door handles high up in the car’s C-pillar. So until you look carefully and spot the rear handles, it could pass as a three-door. The idea is that it looks like a sporty three-door but has the practicality of a five-door.

Diagnosing starting faults often requires a mechanic familiar with a particular make and model who will know where to start looking, as there are literally hundreds of causes for behaviour like this. An auto electrician can also be your best friend at a time like this.

However, as a very rough guide, the problem could be to do with something in the engine bay getting hot and not allowing the engine to restart. The symptoms bear this out; no hot start, but play resumes once things have been allowed to cool over time. Suspicions would be drawn to the ignition system, and a dodgy spark plug, distributor, ignition lead or coil-pack can easily create this sort of problem. In fact, the coil-packs on your car would be a very good place to start looking, as they have a reputation for cracking and putting a stop to things, especially when they’re hot.