Alright, the Earth has only one mechanism for releasing heat to space, and that’s via (infrared) radiation. We understand the phenomenon perfectly well, and can predict the surface temperature of the planet as a function of how much energy the human race produces. The upshot is that at a 2.3% growth rate (conveniently chosen to represent a 10× increase every century), we would reach boiling temperature in about 400 years. https://dothemath.ucsd.edu/2012/04/economist-meets-physicist/