My 2013 Holden Barina Spark is having trouble starting after a short time turned off

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.