We would use far more energy.
Ad tech will start segmenting right down to the individual customer, burning thousands of watts to work out how to entice then to spend $20.
Perhaps raw heat, rather than the indirect heat effects of global warming will be our next challenge.
The only way to get significant reduction of consumption is via catastrophe. There's a good chance that'll happen, but there's no feasible different way that I can see. Take away large levels of comfort from large amounts of people, and you will inevitably see bloodshed. (Yes, I know that unsustainable consumption will also lead to catastrophe. Welcome to the 21st century, where the path forward is narrow and uncertain, while the stakes are higher than ever)
Though there are some people working on beaming heat into space, I suspect they haven’t fully accounted for heat absorption by atmospheric dust.
The sun deposits enormous amounts of energy onto earth every single day: Around 340 W/m² (averaged over the whole earth), or a total of 43 x 10^15 Watts. Essentially all of it is radiated back into space (mostly as infrared). We have a temperature equilibrium because energy intake is largely constant (surface/cloud albedo notwithstanding) while radiation back into space grows with fourth power of (surface/atmospheric) temperature.
Current global energy consumption is on the order of 2 x 10^12 Watts, over four orders of magnitude lower. If we somehow increase energy production by ~two orders of magnitude, to the point of ourselves emitting 1% of the solar energy intake on top, the surface temperature would need to rise by about 0.75 °C to maintain equilibrium. An order of magnitude more (i.e. three orders of magnitude above current consumption, roughly 10% of solar intake) would correspond to a 7.2 °C rise.
(Point of reference: Global power consumption has barely doubled in the past 40 years. No telling what "free" energy would cause though.)
Presumably we'd have geo-engineered a solution by that point, but it's surprisingly not too early to start thinking about the problem!
You probably can drop an order and a half of magnitude off of that number just based on concentration. And if you don't think 'free' fusion will cause us to use several times more power than we currently use, then I don't know what to tell you.
Absorption and emission bands matter. They are in fact made of exotic materials (rare earths IIRC) so it’s at least plausible.