0 Celsius? Space is far colder than that. Did you mean 0 Kelvin?
We would all be very dead very fast. At 0 Kelvin the fundamental atomic particles have no motion. The heat of the earth primarily comes from our sun, and without that the geothermal heat would not be nearly enough to keep us warm and alive before the magma under the crust itself cooled off.
In ELI5 terms - space is colder than ice or even snow. It’s so cold that it would even freeze lava! Without our sun, the earth would get so cold that everyone and everything on it would turn to ice.