You don’t want to let it soften by warming, you want to soften it by beating it. The idea is to break up the crystalline structure of the butter in the dough so it becomes pliable, but without letting it actually get up to room temp.
Put the lump of dough on a floured board and start whacking it with your rolling pin. give it a series of firm, even, parallel whacks across the width of the lump, then turn the lump a quarter turn and repeat. Turn the flattening lump over and do the same to the other side.
Eventually, all of this abuse will make the butter in the dough plastic enough to roll while keeping it cool. If the dough ever gets close to room temp it’ll become a mess to work with and the texture of the baked crust will suffer
So just go show it who’s boss and work off some of those work-week frustrations at the same time.