That would depend on what you consider "cool" to be. The world has been cooling almost since it first formed and it is still cooling today. So, there is really no answer to your question, unless you want to restate it to something like "how long did it take for the earth to cool to its current temperatures?". In that case, the answer would be the same as the age of the earth, or between 4 and 5 billion years.
The Long Earth was created in 2012.
Long Cool Woman in a Black Dress was created in 1972-04.
It takes a long time
It takes a long time
It takes a long time
The Long Fall Back to Earth was created on 2009-04-21.
The Earth formed 4.6bn years ago, and the temperature of the core is currently 5200°c, and it's projected to go cold in something like 90bn years time, which is irrelevant as the Sun will turn into a Red Giant in around 5bn years time, engulfing the Earth and completely destroying it, so to answer your question, it takes a VERY long time for the Earth to cool down- so long in fact, that it will actually NEVER cool down.
Short answer: No. Long answer: No it was not.
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No, but some scientists do study how the earth, the solar system and the universe came to be based on observations of the universe today and in the past and our understanding of the "laws of physics."
IT took the earth this long to cool enough to form rocks