Scientists use climate proxy records like coral skeletons, tree rings, glacial ice cores, and sediment layers. For example, the levels of oxygen 16 in a layer of ocean debris and fossils go up as temperatures rise. So a high level of oxygen 16 in sediment from one layer tells scientists that the planet was hot and watery when the sediment was laid down.
those records aren't granular enough to say what day was or wasn't hotter. tree rings, sediment cores show things on a seasonal basis - and there's a lot of days in a season