You see the size of the red squares compared to the size of the dessert?
I would imagine we will be using ~500x in 2516, a doubling every 55 years. All of earths deserts and more would need to be covered, even at 100% solar cell efficiency.
edit: global energy use has actually doubled every 20 years recently https://gailtheactuary.files.wordpress.com/2012/03/world-ene...
Before the oil shocks in the seventies, oil production and use was more than doubling every decade. [1] If that kind of energy growth resumed unabated, then in about 200 years we'd be producing about as much power as the Earth receives from the sun. We'd cook in our own waste heat, no CO2 required.
https://en.wikipedia.org/wiki/Petroleum_industry#/media/File...
E = mc^2, so convert the energy into mass and shoot it into space?
To maximize the heat radiated away, you'd need radiators with as much surface area as possible with an unobstructed view of the sky (no cloud cover). They'd also need to be as hot as possible, because thermal radiation power rises with the 4th power of absolute temperature
There have been attempts to detect such thermal radiation from alien civilizations[2].
[1] https://en.wikipedia.org/wiki/External_Active_Thermal_Contro...
For instance, at some scale solar would need to be placed over plants, ergo CO2 problems again.
And at some scale (hugeeeee scale), even wind energy disturbs nature's air currents and would likely cause pretty big problems there too.