Who invented the first heat engine?
In 450 BC, Archytas of Tarentum used a jet of steam to propel a toy wooden bird suspended on wire. This was the first heat engine with a clearly recorded inventor.

Depending on your definition of heat engine, the fire pistons used by tribes in southeast Asia and the Pacific islands to kindle fire could be considered even earlier heat engines. Fire pistons heat air by rapid adiabatic compression to ignite a piece of tinder, which is then used to set light to kindling. The exact date they were invented is unknown, but they are believed to predate 1500 BC.