You are asking the wrong question for the problem at hand. It is the *luminosity* of the sun that determines earth's temperature, not its temperature. And you can see from the diagram below that during formation the temperature always increases when approaching the main sequence (the curve always goes towards the left, never towards the right), so the temperature has always been lower in the past than it is now. But the luminosity (the vertical scale) has been going up and down according to the evolutionary model of the sun, and during a certain period it was indeed lower than it is today.

[![enter image description here][1]][1]

The fact that the earth appears still to have had liquid water during this time is now attributed to the 'Greenhouse Gas Effect' due to the increased levels of $CO_2$ in the earth's atmosphere, but [other explanations for this][2] have been proposed. 


  [1]: https://i.sstatic.net/v3NKF.jpg
  [2]: https://en.wikipedia.org/wiki/Faint_young_Sun_paradox