2005 Opel Corsa Coolant

Hop in and drive like nothing happened. Call the shop right away to tell them what happened. If you wait a day or two, they can rightfully assume you did something long after leaving their shop. When you call right away they will know it was their mistake and they deserve the chance to make it right. Any reputable shop will do that to keep you happy. Please don't be angry with them. Doctors make mistakes too, but mechanics are held to much higher standards.

The coolant is half water and half antifreeze. Adding a half gallon of straight water means there's a quart of water in there that is supposed to be antifreeze, and that is not nearly enough to lose sleep over. Your mechanic will check the freeze point which I'm guessing will probably be around minus ten degrees Fahrenheit instead of minus 35 degrees. Even if it's minus fifteen by you, it won't freeze solid. The coolant will just turn to slush. If the reservoir is empty now, leave it that way. Once everything else is checked over, your mechanic can add straight antifreeze in the reservoir to replace what was lost. It will get drawn in and out of the cooling system each time you warm up the engine, and will be sufficiently mixed within a few days. After that, stop back at the shop at your convenience to have the freeze point checked once more.

Actually, I should have mentioned to keep an eye on the temperature gauge if you have one. Anytime enough coolant is lost or drained out, an air pocket can form under the thermostat. On a lot of engines that air has to be bled out manually. That is done by opening a bleeder screw on the thermostat housing, (which is usually at the end of the upper radiator hose), or by momentarily removing a sensor or threaded plug near that housing while the coolant is being filled. If you drive the car even once and it doesn't overheat, that air is already bled out by itself.

The reason that can cause overheating is thermostats have to be hit with hot liquid to open. Hot air won't do it. If the thermostat stays closed, the coolant can't circulate to the radiator, and hence the overheating. Bleeding that air out is rarely very difficult but failure to do that when necessary can lead to overheating. A lot of thermostats have a tiny bleed hole built in to let the air escape so it comes out as you fill the radiator.