It's not a question of cooling it. It went into a runwaway greenhouse effect (https://en.wikipedia.org/wiki/Runaway_greenhouse_effect) and it lacks hydrogen. All the hypothetical oceans oxygen bonded with carbon and hydrogen/water vapor was blown off by solar wind. The underlying cause was the loss of the protective magnetosphere.

Also, you are probably looking more to continent or small moon size quantities of ice (if that even works, and if the magnetosphere issue was somehow addressed) that metropolis.