What a heated bed is actually for
Holding the lower layers above the temperature at which the plastic pulls in.
A heated bed exists to keep the bottom of a print warm enough, for long enough, that it cools at close to the same rate as the layers printed above it, rather than letting the very first layers plunge to room temperature and lock into their shrunken size while the rest of the part is still hot and still shrinking.
The physics of even cooling
Without a heated bed, the first layers of a print touch a plate at room temperature and lose their heat almost immediately, cooling and shrinking to close to their final size within moments of being laid down, while the layers printed on top of them are still hot with most of their shrinking ahead of them. The bottom of the part effectively finishes changing size long before the top does, and because the two are joined together as one solid piece, the still-shrinking upper layers drag on the already-fixed lower ones as they continue to contract, and that mismatch is exactly what pulls corners upward off the plate. A heated bed keeps the plate itself warm, often close to the temperature at which the plastic stops behaving like a stiff, fully cooled solid, so the bottom of the print stays soft and able to keep shrinking in step with the rest of the part for longer, rather than freezing into its final shape while everything above it still has changing left to do. It does not need to hold the plastic anywhere near its printing temperature to do this, only warm enough that the bottom layers remain slightly pliable rather than fully hardened for the first crucial stretch of the print, after which enough of the part has built up around the base to hold it flat on its own.
The hot-dish comparison
Setting a hot glass dish straight from the oven onto a cold, wet section of counter is a familiar way to crack glass, because the face touching the cold surface loses its heat and tries to contract almost at once while the rest of the dish is still hot and still expanded, and glass has very little give to absorb that mismatch before it fails. The crack always starts at the boundary between the suddenly cooled face and the still-hot body above it, precisely where the two are being asked to be two different sizes while still joined as one piece. A cold, unheated print bed creates the same sudden step in temperature at the bottom of a print, and a heated bed exists mainly to remove that step, so the base of the part is never asked to be dramatically colder, and therefore dramatically smaller, than the layers sitting directly on top of it. Plastic does not shatter the way glass does under that kind of shock, but the underlying mismatch between a suddenly cold, fixed layer and a still-hot, still-shrinking one above it is the same mismatch, only released slowly as a lifted corner rather than instantly as a crack.
The number that matters here
Warming a bed to somewhere around the temperature of a hot bath is often enough to keep common printing plastics soft at the base for the first several minutes of a print, which covers exactly the period when the most corners and edges are freshly laid down and still vulnerable to being pulled up before the surrounding layers have built up enough to hold them flat.
Why this matters in practice
A heated bed does not stop a part from shrinking, since the plastic still cools and contracts by the same total amount by the time it reaches room temperature, it only slows down how quickly the bottom reaches that final size, buying time for the rest of the part to be built up around it before the mismatch between old and new layers becomes large enough to lift anything. This is also why turning the bed heat off part way through a long print, once several dozen layers have already built up and pinned the base in place, causes far less trouble than leaving it off from the very first layer, since the mismatch it is guarding against is worst right at the start and steadily less important the taller the part grows.