New
#11
Theoretically the internal cooling should be sufficient. In reality they're not always that great. From new the cooling systems on a laptop tend to work satisfactorily, but once the heatsink inside is coated with dust it dramatically reduces the potential of thermal conduction, and the dust can also block up the heatsink completely, blocking the airflow.
If you're buying a new laptop then you don't necessarily need to know this now, but it might be worth bearing this in mind in future.
If you have no plans with the old laptop, it might be worth experimenting with it to see what the problem is, and you'll learn something in the process! If you download RealTemp and monitor the laptop temperatures, if the laptop always turns of at a specific temperature threshold then you have an overheating problem. In which case, you could have a go at taking the laptop apart and cleaning any excess dust from the heatsink. (If in doubt, there are normally great tutorial videos on YouTube which will help you do this).