Maybe counter-inuitive but someone posted (I don’t remember who or where, probably on pizzamaking.com) that bulk fermenting dough like this at room temperatures effectively insulates the dough from dropping to fridge temps when you later cold ferment, what with all the bubbles.

The dough should already have warmed up from both the cold strike water equalizing with the other ingredients to a target temp, and the kneading further raising the temp.

Just throw it in the fridge immediately.