As hot as it needs to be. Different CPUs have different temperatures they can run at safely. You'll generally find that in documentation on the CPU.
A good Heat sink will be able to bleed heat off the CPU effectively and never let it get too hot.
As a good rule of thumb however, never let them get over 65 Degrees Celsius. Again, this is "most" cases. Not all. Check with your hardware manufacturer.
To sink the heat.
Heat sinks are very important components in computers. The purpose of heat sinks in computers is to keep the computer from overheating. The heat sink removes heat from the processor, keeping the processor cool.
Heat sink
A heat sink is designed to disperse and transfer heat coming from a processor to an outside medium, so that it does not overheat the actual processor chip. It is usually used in conjunction with a fan to cool the device it is installed on.
To cool the processor
heat sink
It keeps your processor from melting. Do not run a PC without a heat sink on your processor. Processors can get to extremley high temperatures. The heat sink absorbs this heat and removes it using a fan.
The heat sink absorbs the heat from the processor and then the fan disperses the heat.
Heat sink
A heat sink is a device commonly used to help move heat away from a processor. It consists of metal fins that absorb and dissipate heat generated by the processor through conduction and convection. In some cases, a fan is attached to the heat sink to enhance heat dissipation.
sink
If you buy a retail boxed processor, yes. You do get a heatsink fan (HSF) with the processor.