Wasn’t there a Star Trek original series episode where they got too close to a star and everyone was sweating on the bridge?
Yes............
When *wasn’t* there. LOL... there was the NG episode (geek meters are going crazy at LLL) where an alien scientist had developed a shield that made trips through stars possible, and that was revisited in one of those “just let her do it maybe that will shut her up” episodes where the ‘real’ doctor used the method to elude destruction by some alien ne’er-do-wells.
And, when Worf was serving on his brother’s Bird of Prey during the Klingon civil war, they splashed another Klingon ship by leading the other captain too far into the gravity well. No idea why anyone would fall for that, probably just a production ruse to build a cool special effect scene. :^)
The real danger is the Tox Uthat quantum phase inhibitor, that should only be tested in other stars.