I have heard (from an auto store clerk) that running just water will cause overheating.
Well, that's not true. Water isn't the cause of overheating. Your coolant mixture (of whatever proportion) and radiator work together to get rid of the heat. If it's not hot, you won't overheat. However, when it is hot, the coolant can only absorb heat up to its boiling point.
Here's a super high level summary of a cooling system:
- The cool coolant is placed in contact with the metal of the hot engine.
- Heat is transferred from the metal of the engine to the liquid coolant, heating it up.
- Hot coolant is pumped to the radiator, making room for cooler coolant to move into the engine.
- Hot coolant is placed in contact with the metal of the cool radiator, cooling it off.
Liquid cooling requires the best contact possible between the metal and the liquid for most efficient heat transfer. Problems occur as the coolant approaches it's boiling point: steam bubbles start to form, especially at hot metal surfaces. Each one of those bubbles is a less efficient point of heat transfer. That means less heat leaving the engine, meaning a hotter engine, more spots where bubbles will form, repeating until steam starts coming out of the hood.
So, one of your main goals in assembling a useful cooling system is to ensure that the boiling point of the coolant is high in order to prevent high temperature disaster. Water's boiling point is 100 C = 212 F. Straight ethylene glycol's boiling point is at 197.3 C = 387 F. Of course, you shouldn't use straight ethylene glycol in the radiator either for the sake of efficiency.
The clerk also said that antifreeze prevents corrosion and sediment build up and cleans the coolant system.
That depends on the product. Quite a lot of the coolants on today's market will inhibit corrosion and minimize sediments. Some, like Water Wetter, will actually increase the cooling system's ability to carry away heat.
Despite years of using water in the summer, I have never experienced any problems that were obviously related.
Just remember that lack of evidence doesn't necessarily indicate absence of the phenomenon.
Do I need to start using antifreeze, even in the summer?
As always, it's your car. You need to make the call. I can't be bothered to flush out my coolant just to change it from green to clear. When it's dirty, I flush it, not before.
NOTE: I know that a pressurized radiator system changes the physics from this simple "boiling point and no higher" explanation. This is a reasonable first-order approximation for the purposes of discussion.
EDIT: @Paulster2 was kind enough to post a picture of what happens to a water pump when it is run with straight water without the corrosion prevention of coolant + water: