I am just saying about my current computer. If needed, I will buy a desktop. I don't need high-end graphic card.
There are noiseless silent notebooks too, but difficult to find and hardware is not so great. If I were you I would look for silent PCs with no fancy graphic card.
Do that. I run Dell workstations. They are not "silent" but low enough noise to live with. You can get competent ones on eBay for a few $$$ Hundred. I have 4x, T5810s in my home network running W10. When I bought them on eBay, they were $225. You might use that as a reference as to what computer to get and what to pay for it. For trading, I recommend Dell Precision Line of workstations (their best, IMV). Have used them for years. Even my laptop is a Precision model. HP has equivalent models which you can check out at Newegg.com.
Here is one example. The key is "CPU Cooler: Noctua NH-P1 Fanless Cooler". https://silentpc.com/fanless-pcs/fanless-tower-intel
My Dell Workstation laptop at work is virtually noiseless, but it also costs around $4.5K, so that's out of my budget range. I have a gaming laptop which I use for my trading and it is noisy at times. I've considered upgrading to a desktop machine because of that and I would also feel more comfortable with a desktop running 24/5 during the trading week.
The Fan speed in a notebook depends on the temperature sensors on the notebook. They are usually factory set and I would not tinker with those. You apparently run software/processes that stress the cpu or gpu which cause temperatures to rise. You should probably invest in a desktop pc if you need more demanding workloads.
Late to the party. Just adding a few words. If you are planning to buy a new one look for a "fanless PC". They dissipate heat though a special metallic case. If you want to fix yours have a look at videos like: