Only 70% of the incident sunlight enters the Earth’s energy budget—the rest immediately bounces off of clouds and atmosphere and land without being absorbed. Also, being land creatures, we might consider confining our solar panels to land, occupying 28% of the total globe. Finally, we note that solar photovoltaics and solar thermal plants tend to operate around 15% efficiency. Let’s assume 20% for this calculation. The net effect is about 7,000 TW, about 600 times our current use. Lots of headroom, yes?
When would we run into this limit at a 2.3% growth rate? Recall that we expand by a factor of ten every hundred years, so in 200 years, we operate at 100 times the current level, and we reach 7,000 TW in 275 years. 275 years may seem long on a single human timescale, but it really is not that long for a civilization. And think about the world we have just created: every square meter of land is covered in photovoltaic panels! Where do we grow food?
To very TL;DR things: solar and tidal energy (and their derivatives like wind) are essentially the only sources of energy we can rely on as our energy requirements grow. We are shockingly close (~300 years) to measurably raising the equilibrium temperature of earth's surface through purely thermodynamic effects if energy use trends continue. This is completely independent of greenhouse gases, and assumes that Earth is a perfect blackbody radiator. Once we exhaust our energy budget from these sources, that's it. No magical unobtanium source of energy can solve the fact that producing additional energy on the surface of the Earth will raise its temperature. We will stop increasing our energy use one way or another once we hit this wall.
If we want to continue using more energy we'll need a whole second Earth to do it on. Great, we've colonized mars! What does that get us? Based on a 2.3% growth rate and the Rule of 70[3], we'll use up that second Earth in thirty years. We'll now need two Earths to keep growing for the next thirty years.
[1] https://dothemath.ucsd.edu/2011/07/galactic-scale-energy/#:~...
[2] https://www.youtube.com/watch?v=F-QA2rkpBSY&pp=ygUodGhlIG1vc...