No, HP is punting. They designed the laptop, they are the integrater, they made the laptop, and they are responsible for support of your hardware. Return it to HP for warranty replacement or repair.
"HP support recommended contacting Intel" .... really they did say that?
After performing basic troubleshooting like cleaning air vents, placing the laptop in a well-ventilated area, adjusting fan/cooling settings in BIOS, updating BIOS firmware and drivers, etc... this then maybe is pointing out to a hardware issue... the common case would be an integration issue between the processor and the rest or hardware components and (poor) cooling design, and this is something done by HP, not Intel, the only ones that can check this configuration is HP... In the worst scenario and less common would be that the CPU might be defective, hence HP is the only one that can assist you with warranty support for a CPU on HP laptop as Al.Hill said before.
I have correspondence on WhatsApp (number taken from the official HP website) in Russian
Everything you wrote is done. The new laptop (paid 2 weeks ago) in the BIOS there is no way to configure fans. BIOS updated to the latest version recommended by HP
In Russia, winter, the temperature in the room is 20 degrees Celsius. If you disable turbo boost, the laptop works perfectly at a base frequency of 2.4 GHz.
something like this.
After doing basic trobleshooting, it is not normal to experience this issue on a new laptop, Also, you shouldn´t have to disable turbo boost to have it working fine.... Contact HP to assist further with this, if they don´t assist further, return the laptop and get a new one from another manufacturer...