Is the heat produced by fossil and nuclear fuel negligible?

Let me borrow an image to put some numbers around it:

So, in one hour, the Earth receives more energy from the sun than us humans generate in an entire year. If we took all of the energy we generated over a year (and not just the waste heat) and converted it into heat, we wouldn't even be adding half of one percent to the system. Our direct contributions to the system are minuscule. The problem is we're pumping out green house gasses like there's no tomorrow. And those directly increase the amount of solar energy the Earth retains. And when we start keeping 1 or 2 more percent of that insane amount of solar energy, it adds up really, really fast.

Humans generate 4,000 terawatt hours of electricity in a year. The sun dumps nearly that much on earth in 1 minute. That's a 6 order of magnitude difference. So I'm going to assume that human heat generation is probably negligible.

Its not the question you asked, but Nuclear plants can raise the temperature of the bodies of water they use for cooling nuclear plants. Additionally climate change is reducing water availability needed for nuke plants which is something I don't hear the nuclear advocates talk about when we're facing a dryer and hotter future. We'll have to start turning off nuclear plants right when we need them.

This is already happening occasionally in the last decade:

Lochbaum analyzes reports from the NRC showing when nuclear plants scale back generation because of warm water.

In June, nuclear plants in Georgia, South Carolina and Pennsylvania scaled back their generation multiple times because of hot temperatures warming their cooling water. The Limerick power plant on the Schuylkill River near Philadelphia has scaled back because of high temperatures frequently over the past decade, according to the reports.

The Dresden and Quad Cities plants in Illinois had to scale back because of high water temperatures multiple times over the past five years. The Duane Arnold plant in Iowa and the Monticello plant in Minnesota also reported scaling back generation because of temperatures.

source

That heat is kinda overshadowed by the giant ass ball of fusion shitting metric shit tons of energy at us.

It got a bit technical in the middle. Hit me up if you need that ELI:5.

Yes, it's negligible. Before considering atmospheric attenuation, every day something like 15,000,000,000,000,000,000,000 Watts (15 Zettawatts) of the sun's power reaches the earth. SOURCE

So enough power hits the earth in a second to power the human population's activities for many months at a time.

You would think that's enough to put into perspective how bad energy trapping atmospheric emissions are, but nope.

The greenhouse gas "problem" is necessary to survive. If the greenhouse effect didn't exist, neither would life as we know it.

The issue with combusting non-renewables is that that energy used to be sequestered away from the carbon cycle, effectively allowing for a balance without too much overall disruption (certain natural events notwithstanding).

So now, with all this stored away, not-part-of-the-carbon-cycle carbon being burned up, we're adding more to the carbon cycle, disrupting it, and causing a new higher thermal equilibrium (which has yet to be reached due to geological time scales). Side note: water is a better greenhouse gas than methane or carbon, but it's accounted for.

Because the greenhouse effect still exists, and we're adding more greenhouse gasses, the greenhouse effect will not allow heat to transfer to space as easily.

With solar being "captured" by a black roof, that would be mostly negligible, as a portion of that energy will potentially radiate away during the capture process. However, with more greenhouse gasses being dumped into the atmosphere, that radiative cooling will become less viable as time goes on, as it too will stay largely captured.

We need to reduce greenhouse gas emissions, otherwise it'll cause a runaway effect. That part might be too late.

I'm not exactly sure of the context of the question.

Electricity plants use the excess heat for district heating. It isn't just wasted. If we could suddenly stop using coal or other combustibles for electricity production, we'd still need to produce energy for heating.

Transport is different though. Gasoline engines are highly inefficient and produces a lot of excess heat that isn't used even when the heater is on full blast. It's not much in comparison to power production though, so while it will be more efficient to drive and heat a car by electricity, excess heat from cars isn't really an issue in itself. It's the pollution that is the main issue.

As for solar panels I think the word you're looking for is "albedo"

Off the top of my head I think it's close to earth's natural albedo anyway. Or even if it is a lower number and more energy/heat is absorbed it's so negligible. Only the tiniest fraction of the earth's surface would be/are covered in panels

Given a radiative forcing coefficient of ln(new ppm/old ppm)/ln(2)*3.7 W/m**2 I have previously calculated that for every 1kWh of electricity generated from natural gas, an additional 2.2 kWh of heat is dumped into the atmosphere due to greenhouse effect in every year thereafter (for at least 1000 years that the resulting carbon dioxide remains in the air). So while the initial numbers are similar, you have to remember that the heat you generate is a one-time release (that dissipates into space as infrared radiation), but the greenhouse effect remains around in perpetuity, accumulating from year to year. If you are consuming 1kW of fossil electricity on average, after 100 years you are still only generating 1.67kW of heat (1kW from your devices and .67kW from 60% efficient power plant), but you also get an extra 220kW of heat from accumulated greenhouse gas.

I have wondered this question myself, and it does appear that the heat from the fossil/nuclear power itself is negligible over long term compared to the greenhouse effect. At least until you reach a Kardashev type I civilization level and have so many nuclear/fusion reactors that they noticeably raise the global temperature and necessitate special radiators.