The car throws white smoke after being driven for about 5 minutes and gets really hot.

Where's that smoke coming from? If it's blowing out of the tail pipe, suspect a leaking head gasket, or less commonly, a cracked cylinder head. You'll also notice the coolant level going down in the reservoir.

The valve cover will get hot because it sits right over the exhaust manifold.

You might be seeing coolant seeping out and vaporizing but it's impossible to say without seeing it. The clue is whether the coolant level is going down. Other things can cause smoke too. Overheated electrical wires and engine belts can smoke but there will usually be other symptoms too.

A cracked head can be repaired if necessary, but it's fairly expensive because it requires welding and machining aluminum. That is reserved for rare or valuable parts. For most engines cracked heads are just replaced. Some engines are well-known to develop small harmless cracks that do not need to be repaired. A corroded and leaking head gasket is much more common. That is considered to be a normal repair. Usually though the leak lets coolant get into the cylinder and go out the tail pipe. It's less common, but possible, to leak outside the engine.