I guess that energy will be used up and, at the end, will contribute to heat the earth, so I see no big differences... please explain your point of view.
Taking the question at face value, the answer is yes. In order to collect all the solar energy arriving at the Earth you would have to completely cover its surface in solar panels. These solar panels would have to encase the entire atmosphere, because otherwise some energy would be reflected by clouds. This would leave no energy left to drive photosynthesis, which would very rapidly change the atmosphere's composition - we'd run out of oxygen unless we used some of the energy to make more. There would also be no energy to drive the water cycle, the ocean circulation or the wind. In short there wouldn't be a climate any more.
However, let's instead assume a more sensible scenario and say that humans only decide to extract all the solar energy that reaches the surface of the Earth in places that are currently deserts, so that most of the plants on Earth are still able to survive and we could still feed ourselves using agriculture. This would produce far more energy than we currently use. Whether this would have a substantial effect on the climate is not obvious. It would heat those regions up a bit (since deserts currently reflect quite a bit of sunlight back into space) and maybe this would cause changes in weather patterns. However, the main consideration would be what effect this would have on greenhouse gases. That depends on what we use all that extra energy for, and whether we keep on using fossil fuels at the same time, so it's pretty hard to answer.
If humans were able to catch all sun energy reaching the earth for their use, will the climate change? It would depend on how much of that energy ends up as heat. Currently, a proportion is reflected back into space: the Earth has a non-zero albedo - it is not perfectly black, and does reflect back into space. Pretty much all the rest does end up as heat.
If we were to capture all of the incoming solar energy, effectively making the earth's albedo zero, then it would depend on how much of the energy ended up as heat, and how much of the energy became embedded as chemical or other potential energy (to take a ludicrous example: we could use the captured solar energy to lift boulders up Everest). If the same amount of energy ended up as heat as it does now, and if the geographic and temporal distribution of heat were the same as it is now, and if the content of greenhouse gases in the atmosphere stayed as they are now, then the climate would not change at the scale of a human lifetime (but would continue to evolve at the scale of thousands to millions of years).
If, however, the distribution of heat changed, or the total amount of heat changed, (or both changed), then the climate would change within a human lifetime. Just as it is changing now, within a human lifetime, because of the dramatic increase in concentrations of greenhouse gases.
If all the incoming solar energy were ultimately converted to heat on the Earth's surface and we totally prevented the Earth from radiating thermal radiation, the temperature would be going up by something close to 1 °C a day or so – the same warming we experience every day (and the cooling at night).
More realistically, the Earth has to radiate thermal radiation. Still, if all the incoming radiation from the Sun were converted to heat and radiated as thermal radiation, the Earth would effective have no albedo (no reflectivity) and the temperature would go up by a hundred of degrees because right now, the albedo is 0.37 or so which means that some energy is reflected.
If you're more modest and you keep the albedo, then nothing changes about the heat transfer. Instead of going to solar panels, the energy may go into crops of the same color.
But let me return to the other part of this thought experiment, i.e. to the question how the energy is used. All the "ifs" above are unjustified. It is not true that – as you write – all the energy we would get from the omnipresent solar panels would ultimately be converted to heat. We are doing lots of other things with the energy. For example, we use fluorescent light bulbs, so some of the energy is radiated – partially to outer space – in the form of "cold light" at visible frequencies. The light that our light bulbs from the cities emits to outer space – which you see from an airplane – doesn't contribute to the change of the temperature on the Earth.
Even more importantly, a part of the energy is used to move matter. When we build skyscrapers, we may use electromagnetic motors. So a part of the solar energy would be going to the potential energy of stones and bricks in the buildings – into the increase of height non-uniformities on the Earth's surface.
So you should be better very careful about the diverse possible fates of the energy. On one hand, you're right that if (dark) solar panels replace (lighter) plants or ice/snow on the surface, we will be getting more energy from the Sun. But on the other hand, it's not true that all this energy gets ultimately changed to trapped heat – you shouldn't forget light escaping to space and potential energy of rocks and water, among other things.
I kept a statement to the very end. What matters for the temperature of the Earth is not just the albedo; it's the "greenhouse effect", too. You may still compare the situations in which the energy is obtained from solar panels; and from fossil fuels. If there will be enhanced greenhouse gases, it's more likely than not that the effect of the extra greenhouse gases in the atmosphere will be somewhat greater than the change of the albedo from the solar panels. One has to do the full calculation to settle this question. But even as a climate skeptic, I have to warn everyone: the change of greenhouse gases modifies the equilibrium temperature of the Earth "permanently" (well, for a hundred of years or so) each time we burn a gigaton of carbon; on the other hand, the absorption of energy by a solar panel only changes the energy budget on a one-time basis.
At any rate, all those discussions above are academic in character. In the real world, the changes of the temperature by a changed albedo or changed concentration of greenhouse gases are so small that we can't really isolate it from other, mostly stochastic changes of the temperature on Earth and from each other. Over the centuries, we may have modified the equilibrium temperature of the Earth by changes to the greenhouse gases; and by tenths of a degree by changes of the albedo, too. None of those things can ultimately compete with the glaciation cycles that are driven by astronomical processes and that dominate the temperature changes at the 10,000-year or 100,000-year timescale.
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