External monitor heating up my MacBook Pro

I have a cheapo (but 1080P) Acer 27" monitor that I use as a reference monitor on my desk. I hook it to my 2013 MacBook Pro via the HDMI port. Works great, but the battery drain on my MacBook is enormous. Has anyone else experienced this or know why this is happening? I can’t believe this is normal.

Does the 13” have two graphics processors like the 15”? If so, it is probably switching to the more energy-hungry processor to drive the monitor. The laptop also switches based on if the Charger is connected.
About this Mac will probably give you more of the story.

IIRC the 13" is integrated graphics only.

Sorry, I should have elaborated a bit. It is a 15.4” Macbook, and yes, it is using the outboard graphics processor. It forces use of this board when an external monitor is used . It doesn’t allow use of the onboard graphics unit.

An. I saw 2013 and thought 13”.
Well, that seems to be your answer then.