Civ V suddenly started making my laptop overheat

So I bought Civ V Gold Edition and the BNW expansion about a month, month and a half ago and for awhile it ran great. My computer would get hot but there was no lag or crashing or anything like that, and I played on DirectX 10/11 with all quality settings at their highest.

But in post-victory play of my 4th game, maybe a week ago now, sometimes when I would load my file I'd get unbearable lag. And there was no in-between -- either it ran wonderfully for hours or it lagged from minute 1 and I had to reboot the computer to get it to run properly again. I figured maybe it was messing up because almost everyone left had a lot of cities and insanely huge armies so I just powered through it.

Then I started up a new game and I think I was about 2/3 of the way through when the lag started coming back, except this time my computer would overheat and shut down if I didn't close the game in about a minute. For awhile I was still able to remedy this by restarting my computer, but now it's to the point where every single time I try to play it just kills my laptop. I turned all quality settings to low and tried DX9 and it makes the game run a lot quicker but it still overheats almost immediately. And this is my first game on epic speed so there's not an absurd amount of units even though I'm well over 600 turns. Does the game just crap out if you go for too many turns maybe? Like around 500? Or if you play too long post-win? I'm hoping I'm not just screwed when it comes to playing long games but I can't really think of what else could be destroying my computer. Being late in the game is the only obvious consistent between the files that lagged, and I know my computer can handle the game considering I ran it fine for the first month.

Doesn't surprise me a bit as a laptop just isn't made for running games (for hours and hours).

Some things that might help to delay the inevitable:
Have it plugged in (don't play on battery/energy saving).

Make sure you're having it on a flat surface, wood, plastic or metal; and that the ventilating slit aren't blocked (and free of dust). Don't put it onto any form of cloth of fabric. Not on your bed, not on your lap.

Turn down the game settings (I know you already did); leader scenes, fog of war, anti-aliasing and all kinds of shadows and reflections are super demanding and turning them down/off makes a huge difference (while you can keep resolution and texture quality up easily so everything still looks pretty good).

Also turn off unit movement/combat animations.

And yes, many civs with many units are certainly devastating. Early game turn times are quick but later on it can become absolutely madness. Playing smaller maps only may be a good idea.

With all due respect, I think you missed the parts of my post where I said that I was able to run the game well for a month. I played 3 full games that went smooth, and the 4th was fine too until the post-game. Game 5 is when it's really starting to get awful. I appreciate the help but I don't think it's as simple as fiddling with options. Particularly since for testing purposes I loaded up one of my old files from a tiny map, quick speed game on turn 300 that only has 1 other civ and 1 CS left on the planet and I still overheated. So it seems it's not the amount of turns, units or anything in-game for that matter.

Something has clearly gone seriously wrong with either my computer or the game files, but for the life of me I wouldn't know what. The 2nd game I played was a huge map with max civs and city-states and it didn't crash or lag even once; how could I possibly go from running that to crashing on a tiny map? It doesn't make any sense. You think maybe my bad GPU started overriding my good GPU for some reason? I don't even know if that's possible but it's the only thing with my hardware that I could fathom "unimproving." I don't know what could be wrong with the game either though unless there was a bad patch recently or something. Maybe a reinstall could help? Can you even do that with Steam without paying again?

Automatic energy-saving / gpu-switching / cpu throttling is often a problem with laptops, but that would only cause lag/slow turns. Not turn the machine off.

Since you said overheating I thought it definitely was overheating as in >you checked the temperatures<. Why didn't it overheat previously? You used it differently (see posting above) or too much dust accumulated over time or a radiator stopped working (most tools that check temps usually also show fan speeds) or it simple wasn't as hot at your location during the last weeks as it is now

Sorry I haven't responded, I got a bit busy and then my Internet was acting up for a couple of days.

No I never actually checked the temperatures (I didn't even know you could until I started looking for how to fix this problem) but the computer was scorching hot when it turned off so I figured it was a safe assumption.

I installed SpeedFan and my temp with hardly anything running is hovering between 50C and 60C for the GPU and 60-70 for the cores. When I ran the game I think the temps went up to about 80 and 90 respectively. I don't know celsius or what a good CPU temperature is but 80 and 90 isn't much worse than when I'm watching YouTube in HD or running other large programs and none of that makes me overheat. It doesn't always even make the computer hot.

Is there a simple way to go about checking the radiator? SpeedFan supposedly gives fan speed as well but it's not showing me any. I tried another program and it's the same deal. Other than that, is dust buildup pretty much the only thing that could be the problem then? I've used it in exactly the same way every time so it's nothing like that.

80-90°C Celsius for the CPU definitely is too hot.
YT or other stuff most likely doesn't use up as much, certainly not gpu and cpu power at the same time... or for YT etc the temp is so high without throttling, while with the game on it's taht high even though it throttled itself down, thus the lag.
So maybe the reduced cooling abilities due to 'aging' (dust, a broken fan (hope you are at least still hearing one), fan/heatsink/wlp issues) might just be too much.
Maybe you should have an expert have a look at it?

Ehh, I already had to send it in just a few weeks before getting Civ for a new hard drive, so I'd rather not burn even more time and money so I can play one game. Not sure if I could even afford whatever improvements/repairs they'd wanna make with the ridiculous service charges on top of the cost of good hardware. I guess I'll just clean out the dust and see if I can get anywhere from that. I'm hearing the same noises coming from my laptop as I always have, so if there is a fan problem then I can't tell it. I admit I'm not much of a hardware guy though. But performance hasn't decreased at all while doing any other activities besides Civ.

If you can feel warm air coming out of the side or rear, then the fan is working. You can try propping it up with something that allows air circulation under the unit, and use a small powerful room fan to blow air above and below the laptop.