It's a common misconception that keeping the lid on your grill will make it hotter. In reality, it doesn't make much difference one way or the other. The main reason for this is that charcoal grills are designed to allow air to flow freely through them. This airflow is what allows the charcoal to burn hot and evenly. If you were to completely seal off a grill, the fire would eventually go out due to lack of oxygen.
So, if you're looking to get maximum heat from your grill, it's not going to come from keeping the lid on. Instead, focus on building up a good bed of coals and then letting them burn down to white-hot embers before cooking. That's when you'll really be able to crank up the heat!