There's 2 ways of dealing with high temps on a laptop, and they can be combined if you're feeling lucky. Do the first one first; it's entirely reversible, unlike the second one.
The first way is to
undervolt the CPU, literally feeding it less voltage than stock so it produces less heat. What I use personally is ThrottleStop;
here's a guide on how to use it. Of course, you run the risk of system instability while undervolting, so I recommend doing a stress test on the CPU after you've undervolted it. If it crashes or spits out an error during that process, you've gone too low with the voltage, and you need to raise it by 5 mV. A round of Cinebench R20 is good enough for establishing baseline stability, but what you really want is something like Prime95 on the Blend torture test for at least 24 hours straight once you've dialed in a "stable" undervolt. I'd suggest even longer; I'd go for a whole week if you can.
On my laptop, I started with -100 mV offset on Core and Cache voltages, then I worked my way down to -160 mV, using Cinebench to establish that each successive undervolt was vaguely stable. Thankfully, I run Folding@home, so that's what I used as a stress test. I left my computer on overnight, letting it crunch numbers until it crashed. After a series of crashes due to the undervolt, I eventually converged on an undervolt of -140 mV, which appears to be stable enough to survive an entire week straight.
I wouldn't recommend starting ThrottleStop on startup, though; what I do is place it on the taskbar so that you can open it manually. This is to avoid bootloops if you end up with too low of a voltage setting and end up crashing because of that. If opening TS crashes your laptop, you can delete the "ThrottleStop.ini" file in the TS directory to reset everything back to defaults and try again.
I don't think this voids your warranty; worst-case, you can delete the ThrottleStop directory, and no-one's the wiser.
Please check if your laptop has an Intel or an AMD CPU inside; ThrottleStop works only with Intel CPUs, and to my knowledge, AMD (Ryzen and earlier) has no tools for undervolting laptops.
The second method is to
repaste, replacing the thermal paste between the CPU die and heatsink to increase the rate of heat transfer from the CPU to the heatsink. This is a difficult process, and usually requires disassembly down to the motherboard for a standard laptop. Gaming laptops tend to be easier in this regard. This will almost certainly void your warranty, so do this at your own risk.
The theory is fairly easy once you've disassembled the laptop far enough to see the heatsink assembly:
1. Locate the heatsink.
2. Unscrew the screws holding it to the motherboard and take it off.
3. Clean off the stock thermal paste from the heatsink and CPU die with alcohol (isopropyl alcohol seems to be the stuff of choice, but ethanol works too; I used hand sanitizer myself)
4. Apply thermal paste to the CPU die.
5. Mount the heatsink back on to the board, then screw it back in.
Of course, this is a daunting task for most people. I was positively shaking when I replaced the thermal paste on my laptop. If you do this on a new laptop, prepare yourself for disappointment (at least in my case); you won't see much difference on your thermals, but depending on the thermal paste, it might hold up better over time.
As far as choice of thermal paste, you can't really go wrong with a well-known brand like Arctic, Thermal Grizzly, Cooler Master and so on. If it appears on a list of best thermal pastes, it's probably good enough. Be careful though, you want a thermal paste intended for air cooling, and you sure as hell do not want a liquid metal thermal solution. Without proper precautions, that leads to short-circuits, and can degrade the copper/aluminum on the heatsink itself. I used Arctic MX-4 thermal paste on mine, since it claims that it'll last for 7 years, and that was what I had at the time.