As best as I can remember, the focus of the story is a planet that is in deep/interstellar space, balanced between the gravitational pulls of two distant star systems. One of these is Sol, and I do not remember the other (Centauri or Proxima, perhaps?). The planet's is comprised of a number of frozen chemical compounds that are able to exist in this form because of the planet's unique location. I believe supercooled helium might be one, but I can't say for sure. The relevant point here is that the compounds form the "building blocks" for the planet's development of intelligence.
The first few paragraphs of the story chart the progress of the planet's development. Naturally occurring electrical impulses begin a process where, over the course of several millennia, simple chemicals develop into rudimentary circuits, which in turn become more sophisticated circuits, which eventually develops into a complex, planet-wide matrix. In effect, the planet has become a massive organic supercomputer.
Once the planet reaches the supercomputer stage, it develops an imperative to reach out and make contact. The planet creates icy, comet-like "probes" which it launches into space in the direction of Sol system. I'm not sure how these are launched. I do recall the story details how the first few probes were destroyed when they were close enough to a system that a change of even a few degrees Kelvin was enough for them to dissipate from the heat. Each generation of probe survives just a bit longer than the one before.
This is the sum total of my knowledge of the story. It was either a long-ish short story, or a novella. In either case, I never got around to finishing the tale. Hopefully what I did read is enough to identify the story.
I read this story in the mid-1980s. I think it was in a sci-fi magazine rather than an anthology or collection. I am not certain of that, however.