There are at least two ways to answer this question.
The first way to answer it is simply to state the years in which Thomas Paine lived. Thomas Paine was born in 1737. He died in 1809. This means that we can say that his “time period” was mostly the mid- to late-18th century.
The second way to answer this is to place him in the context of the time in which he lived. In other words, we can say that he lived in the time period of the American Revolution. Thomas Paine was a very important part of that revolution. His pamphlet, Common Sense, is credited with creating a great deal of support for the cause of independence.
So, we can say that Thomas Paine was in the time period of the American Revolution and/or we can say that he was in the mid- to late- 18th century.