There’s a minimum level of energy consumption (and thus heat) that has to be produced by computation, just because of physics. However, modern computers generate billions of times more heat than this minimum level.
The minimum amount of energy needed to compute decreased asymptotically to 0 as the temperature of space goes to 0. This is the reason a common sci-fi trope where advanced civilizations hibernate for extremely long times so that they can do more computation with available energy.
In the book Calculating God, a character notes that this is a common civilization-wide choice. Living in virtual reality, rather than trying to expand into the vast expanses of space, is a common trope as much as it's a logical choice. It neatly explains the Fermi Paradox. In some fiction, like The Matrix, the choice might be forced due to cultural shifts, but the outcome is the same. A relatively sterile low-energy state civilization doing pure processing.
True. But it's not a binary choice. All it takes is to make one sub-optmial choice for the universe to be filled up with von-neuman probes in all star systems
https://en.wikipedia.org/wiki/Landauer's_principle