Fan running when external display is connected

I have a MacBook Air 13in, mid 2011, 4GB memory, 1.7 GHz (iCore 5), running OS X 18.3.

With the laptop on, every time I connect an external display (HP LA2205wg) through a miniDisplay to VGA adapter, the fan starts running wild and it is so loud to disturb my work. Yet, I check the activity monitor (All processes) and there does not seem to be any process taking a lot of CPU.

However, if I swich the MBA off, wait a few seconds for the fan to stop, and then restart the MBA, there is no fan noise. I have to do this every day I get to the office and connect the external display. It's annoying, as I have to reopen the same files etc.

I have browsed the apple support forums and I have seen similar posts, some dated 2009. Yet no actual fix is suggested in the posts. I am still giving it a shot, hoping I don't need to waste even more time to go to an Apple store. Any help would be greatly appreciated.

Mario