Hi all, would this cause over heating/is this bad?

It would help to know what model you have (XPS 9550, 7950, etc.) but the answer is that yes, driving an external monitor at that refresh and presumably high resolution will appreciably stress the system.

What happens to the system's temperatures when the external monitor is not connected?

And if the system is more than a year or two old, has it ever had a thorough internal cleaning and replacement of the thermal pads that sit between the heatsinks and the heat slug on the CPU and GPU?

@ejn63​ Hi! It is an XPS 15 9530. I just got it this past August, so it is coming on a year soon. 

If it helps to include, I normally run the monitor at 60 Hz for power-saving reasons. When it is connected to the monitor but not the power source, it maintains a relatively cool temperature.

It's the added GPU needed to drive that monitor -- it will increase the system temperature, and there's nothing you can do about that.  Unless the system is actually throttling (slowing down), it's not a cause for undue worry.

There just isn't much margin in added cooling in a system as thin and lightweight as this one.  

@ejn63​ Got it. Thank you so much! Also, I do have the computer stored in a drawer under my desk, when connected to my monitor. There is a slit in the upper back of the drawer where the USB-C hub cord and the USB-C charger cord come through which I think is good to make way for the rise in temperature to have a way of escape. However, would you recommend adding more ways for the heat to escape? I.e., drilling holes in the bottom of my drawer? 

@nate893​ 

I would remove the system from the enclosed drawer completely.