While the design is similar to instruments Galileo used to study temperature, the modern Galileo thermometer is believed to have been invented sometime in the 17th or 18th century.
It's thought that the first versions were likely created by artisan glassblowers rather than scientists. The earliest known example of a Galileo thermometer is from 1638, though it's not known if this was the first one ever made.
It's important to note that the term "Galileo thermometer" is a misnomer. While Galileo did make significant contributions to our understanding of temperature, he didn't invent the thermometer that bears his name.