What is it about TS4 that makes a computer run so hot?

I don't think it's an Origin issue for me. As soon as I exit the game my laptop fans immediately stop running. With Origin still on. Then I'll shut down my laptop and get that message that Origin is still running.

Try capping the maximum cpu load from 100% to 99% - made no difference to the quality of gameplay but reduced my maximum temperatures from 99C/100C down to 60C.

I have an older desktop, it does ok for most stuff. But when it comes to playing Sims 4, I have to have a fan sitting next to it to blow away the hot air coming off my computer. I've only recently had to start doing this. If I don't do this, my computer will overheat and shut down, besides that it would be very uncomfortable just sitting this close to it.
(I won't give my age, but let's just say I'm going through the change of life with hot flashes, so it makes it ten times worse).

Try this:

Does your laptop feel like it's running really hard when you play The Sims 4? If it does and you play using the Origin client you can see if this helps:
Open Origin, at the top in the menu bar select Application Settings, Scroll down to Start-Up Options and De-select Origin Helper Service.

See if that lowers your CPU load, mine was running at almost 100% playing the Sims 4 recently and it shouldn't have been anywhere near that. I don't play on a laptop but it fixed the problem for me and maybe it will help you too.

As others mentioned, it is hardware intensive. My old laptop ran it like lava. However, my new one I sprung for a fair bit of upgraded cooling on my new thing so it stays nice and cool. I'd get one of those cooling peripherals or upgrade the paste/etc. if you are tech savvy.

Vlad in swimming pants probably

but yeah i don't really know why but my computer be running like crazy sometimes when i play and sometimes it makes not a sound and there doesn't really seem to be any particular reason either

Origin is the top culprit I look for when my fans start going out of whack when I'm not playing any games. I don't allow origin to run when my computer starts up, but sometimes, it runs in the background anyway and I have to force it to quit through Task Manager. The CPU goes crazy when origin is running!

I play on a 2015 laptop with 46.86GB of mods and about 400 Sims, and I don't have a problem with my laptop running hot.
I make sure my laptop has plenty of airflow, and I keep my Saves and Screenshots folders as empty as possible. I give it airflow by playing with it on two cheap plastic shelves stuck together:
https://live.staticflickr.com/65535/51345265949_e1cc21eefd.jpg

I verified that it wasn't Origin causing the problem by closing it in task manager and playing in offline mode--made no difference in temps

It's CPU intensive as others have said, but my fans tend to stay pretty quiet while playing the Sims and I play in windowed mode (approx. 2560 x 1440) with a YouTube video playing at the same time because my monitor is a wide-screen. The only time my fans really get going is when I have Reshade on in Live Mode. I have an i9/2080 Ti, though.

ETA: What are you doing in the game? If you're building odds things or modding to have a ton of sims on a lot that may have an effect.