That depends on where the water was leaking from....
Water pumps have a hole drilled in them that goes throught to the cavity between the bearings. When the bearing are stuffed the water leaks into this cavity and then out the hole... Telling you it is time for a new pump...
I would also think that if the water is leaking from there then it obviouly traveled through the bearing, whitch now would be cleaned of all lubricant from the water passing through it and quickly destroy itself..
If your car is heating up very quickly then there is a good chance that your pump has failed...
If your pump isn't circulating the water, then all the hot water will rise (cause thats what is does) And tell you your engine is hot... even though really its only hot at the very top top to start with...
Also Bleed your cooling system properly...
Was at a machanic mate place the other day with another friend who had to replace his radiator... topped it up full of water and closed the bonnet cause he was done and my machanic friend was like woohh... You ain't done yet...
Bleed all the air out (took a while) and the car took almost another 6 liters of water..!!!!
If there is an air pocket.... Take your cap off (do this before your engine is HOT) and if an air pocket exists then the water in your radiator will bounce up and down alittle..
Thats what I was told..
He just let it get up to temp with the cap off.. water would spurt out of the rad in short burts then he'd top it up again and repeat again and again till the water stopped bouncing..