It depends on what the exact PSU model is, and overheating would not occur. The first thing to clear is there is no such thing as "not having enough wattage". Wattage is not a stuff, and a power supply is not some kind of squirt gun that shoots out power. A power supply creates direct current, which is a flow of electrons in the case of computers. If a power supply's components are not rated to handle high amount of current, they can burn or melt. PSUs have protections that should kick in if this is going to happen, but they don't always, which is why you find junk 420W units that catch on fire after being loaded to 250W.
Therefore, labelled wattage does not matter! Do not use labelled wattage as a parameter for comparing power supplies.
What is your exact PSU?