"It's renewable therefore I can waste as much of it as I want."
You would need enough demand to create a global shortage. That doesn't seem likely and would cause a short-term spike, not a long term price increase.
https://dothemath.ucsd.edu/2011/07/galactic-scale-energy/
Of course that's more an illustration of why continuous growth is impossible than a prediction of what will happen.
Haven't done any math either ways, but it's not like sunlight doesn't already heat up the planet.
"Cities and their expansive hardscapes are certainly to blame for the heat island effect and, since the hardscapes and solar energy-absorbing roofs are already there, solar panels may actually represent a reduction in heat absorbtion. Add to that the fact that solar panels produce renewable energy that does not contribute to climate change like conventional sources like coal. Adding to that, the soot particles in the atmosphere from the burning of fossil fuels contribute a radiative forcing of 0.1 to 0.4 W/m2. Solar panels, on the other hand, are reducing the amount of climate change-causing emissions.
"So if you're wondering about the heat island effect before installing rooftop solar, don't. According to the numbers, the solar panels will not only produce energy, but keep your home slightly cooler, which means you'll be using less energy in the first place, which will keep us all a little cooler."
If you can get on the grid, then the power your plant produces and what you do with it are two separate things. Instead of e.g. mining crypto, you could sell the power generated. By using it instead of selling it, you're just pushing other users to use more fossil fuels.
The calculus IMO is power consumption * grid-wide average CO2 emissions. You can't just count using solar as 0 emissions, because using solar doesn't bring that average to 0. It reduces it slightly.
This is also too simplified, because it doesn't factor in transmission costs and interconnection capacity. Electricty doesn't move frictionlessly throughout the grid, and this can be seen because north american electricity prices vary wildly by region[1].
There are times when renewables have to be curtailed in some regions, so using renewable sources at that time has a marginal CO2 impact of near zero.