Past performance is not a predictor of future results. If we continue to grow GDP (~energy consumption) at about 1%/y, we’ll boil oceans in 400 years. That’s what exponential growth means.
I'm pretty convinced that increasing human activity so much to increase the background radiation to 373K is never going to happen, the point is more that any exponential energy growth eventually can't continue.
In a way though it's already happening, the GDP ~ energy consumption equivalence from the GP assumption does not hold (https://data.worldbank.org/indicator/EG.GDP.PUSE.KO.PP). We'll just keep inventing ways for the GDP number to keep growing exponentially in questionable ways for the system to keep going, until we can't anymore.
Sure, if you think of the Earth as a game of SimCity plus Kerbal Space Program, these discussions about exponential growth are interesting. However, they miss the part where the intervening 30-100 years become literal hell on Earth while space travel ramps up.
The GP said 400 years. That's the time since the age of exploration until now. That's a vast era of time, and exponential technology development goes both ways.