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Once carbon emission neutrality and other sustainability goals have been achieved, a widespread assumption is that economic growth at current rates can be sustained beyond the 21st century. However, even if we achieve these goals, this article shows that the overall size of Earth's global economy is facing an upper limit purely due to energy and thermodynamic factors. For that, we break down global warming into two components: the greenhouse gas effect and heat dissipation from energy consumption related to economic activities. For the temperature increase due to greenhouse gas emissions, we take 2 °C and 5 °C as our lower and upper bounds. For the warming effect of heat dissipation related to energy consumption, we use a simplified model for global warming and an extrapolation of the historical correlation between global gross domestic product (GDP) and primary energy production. Combining the two effects, we set the acceptable global warming temperature limit to 7 °C above pre-industrial levels. We develop four scenarios, based on the viability of large-scale deployment of carbon-neutral energy sources. Our results indicate that for a 2% annual GDP growth, the upper limit will be reached at best within a few centuries, even in favorable scenarios where new energy sources such as fusion power are deployed on a massive scale. We conclude that unless GDP can be largely decoupled from energy consumption, thermodynamics will put a hard cap on the size of Earth's economy. Further economic growth would necessarily require expanding economic activities into space.