Those liquid green aliens are probably looking at us and going "how can life exist with so much matter in solid form and so cold”.

Well, they have a point. This is why the presence of liquid water on earth is a big deal.

But when the rocks start to melt you have problems.

Tungsten/Carbon based life forms? Solid when most everything else is liquid or gas.

It's very unlikely for life to arise under those conditions. To get life, you need to build a lot of random polymers in a short amount of time (relative to the age of the planet) and the only known way that can happen is in a liquid or a gas so you have diffusion working for you. But after that, to get technology, you need solids.

The good news is that you don't need to have the life arise under the same conditions that the technology exists. It's possible that the planet is inhabited by self-replicating tungsten-based technology that was created by life that arose somewhere completely different.

But the bad news is that we are much less likely to find the aliens than we are to find the descendants of the self-replicating robots they built millions of years ago. And the fact that we haven't found the robots makes it very likely that the aliens don't exist.

Secondarily, thermodynamics and other effects make many processes much less efficient at higher temperatures, examples including engines and solar panels.

They could be using iridium. When we're talking about aliens, we're already in the realm of hard-to-imagine, but it's worthwhile, I think.

Sure, energy in equals energy out at equilibrium, but another option is to have a steady state solution where energy is generated leading to potentially large temperature gradients.

Yes, that's possible. It could be that what we're looking at on the planet surface is the output of a huge planet-sized radiator, with a civilization living in air-conditioned comfort underneath. But the problem with that theory is that you can't actually use the whole planet as a radiator. You can only use the space-facing side. You have to use the sun-facing side for energy harvesting. That temperature gradient would show up in the spectrum, and AFAIK it's not there.

[UPDATE] I don't actually know if current exoplanet observing technology is capable of detecting such a temperature gradient, but given what I know we can observe I'd be a little surprised if it couldn't. A planet-sized energy harvester would make a pretty big dent in the passive thermodynamics, and detecting that should not be too hard. And it would be Really Big News.

This is a great video that touches on your point, the Earth must radiate the heat it receives to stay in equilibrium, even if it uses it to do work in the process.

https://www.youtube.com/watch?v=DxL2HoqLbyA

If we extract the maximum possible entropy of the incoming radiation wouldn't that mean we radiated at high-intensity but low-temperature?

What does that mean?

Everyday objects don't work like that. Saying ice cubes are cold is roughly equivalent to saying that they radiate less heat than the objects around them. If they radiated at "high intensity" then they wouldn't be cold anymore.

"A cold object that radiates heat at high intensity" is a contradiction.

Only for black body radiation do we have a perfect correspondance between spectrum and intensity. But there can be other ways of radiating. Non-black bodies. Antennas. Lasers.

Not even stars are perfect blackbodies.

The protomolecule was able to build structures on Venus. Then again, if your civilization was over a billion years old, all sorts of things might become possible.

That being said, it’s never actually aliens in astronomy. So far, anyway.

What would be an equilibrium if they spend collected energy on some process with low entropy output?

Like what?

I can't think of anything that would make a difference in the long run. Anything they do is still subject to the Second Law and the limits of Carnot efficiency. They can shunt a little bit of the energy off to the side and store it for a while, but it all has to end up as heat sooner or later.