The case does not act as a heatsink. It acts more like an insulator. Heatsinks require direct contact with the component they are cooling. The more thorough the contact is, the better the cooling is, up to a certain point (this is where thermal paste comes in, and once its limits are reached, liquid cooling comes into play, etc.)
A laptop's casing will more closely resemble an insulator than a heat sink. There is not a whole lot of direct contact between the CPU/GPU and the case. Think of a stainless steel coffee travel mug. The air in between the layers of steel insulates the liquid inside, keeping hot drinks warmer for longer periods, and cold drinks cooler for longer periods. The same principal applies to these laptops.
If you want your system to stay cool when the display is closed, then make sure the fan intakes and exhaust are free of obstruction for at least a 2 inch gap away from them.
Some would theorize that the spaces between the keys in the keyboard allow heat to escape, thereby giving the laptop more cooling ability. Such ability would be diminished by having the display closed over the keyboard. IMHO, that theory is more believable to me than the case acting as a heat sink.
For the OP: When you attach an external display to your system, it engages the dedicated GPU in the system. I suspect that having the dedicated GPU on all the time to drive the external display is the biggest cause for your increased temps.