The coolant ratio does affect how the system cools the engine, but probably not as you'd think. Water is a better thermal conductor than is the antifreeze, so it will do a great job of shedding the heat of the engine. Water by itself does boil sooner than an antifreeze/coolant mix, though, so you could expect it to boil over sooner than without the antifreeze.
On the flip side, water does some things which we mitigate with antifreeze. The amount of antifreeze will keep the mixture from freezing down to a certain point, depending on the mixture. Secondly, antifreeze has corrosion inhibitors in it which keeps the natural tendency of water from corroding the internals of the engine.
The normal mixture used is a 50/50 mix of antifreeze to distilled water. If you go a bit outside of that, you are still going to be okay with the coolant itself. Running a mixture of 40% antifreeze to 60% water would still provide freeze protection down to -12°F (-24°C), while the boiling point would not be significantly affected. A 44/66 antifreeze to water ratio only brings the boiling point of the coolant down by 3°F when under 15psi (103kPa) pressure as compared to a 50/50 mix.
I'd suspect the amount of water you added to the system has had no detrimental affect to your cooling system's ability to cool the engine. If you have heat extremes where you live, you may want to get the coolant mixture right. If you don't have a refractometer or antifreeze tester, you may want to invest in one to help you get your mixtures back to right.
If you ran your car on 100% water, it would not run hotter ... until the engine decided to overheat and boil over. You shouldn't be near that with your engine, even if it is running at 110°C. Pure water under 15psi of pressure will not boil over until it gets to 120°C (248°F). Even if your system was at 100% water (which it's not), there should still be plenty of room left before boil over would occur.