Are you using a modded Tualatin, or just plugging an unmodified version in?

unmodified, looks I have lot of research to do, didn't know it is required. Motherboard is Slot 370 btw, not Slot 1 + slotket

The easiest option, if they are still available, would be to buy a modded CPU from the Korean seller on eBay.

There are also some interstitial devices from Powerleap and Upgradeware that you might be able to find if you're willing to spend a LOT of money and be patient

Another great option would be to use a Coppermine CPU, which will probably does what you want.

Edit:
It looks like the modded CPUs are still sold on eBay. When I searched, the item description was "Intel Tualatin Pentium-IIIs 1.26GHz(512K) include On-chip Socket Adapter!!!"

I've never purchased one, so I can't vouch. Maybe someone on these forums has experience with these.

I bought years ago, the P3S 1400 from that seller, it cost less than now, but still more than an unmodified CPU, it works, it works, but only on the motherboards in the list, in my case on an Acorp i815, it doesn't work, while on an ABIT SA6 and on ASUS CUSI-FX it works very well, indeed perhaps better than the 1400S I have on a TUSL2-C.

The mod doesn't seem compatible with 440BX chipset, per seller, and I'm not adventurous enough to try it at the import price. Oh well, I was mostly aiming to stabilize enlarged CPU cooler on my Coppermine that doesn't have IHS. The small fans are whiny so I put a cooler on it that grows upward to fit 80mm Noctua. Silent but I'm not pleased with how wobbly it is. Maybe I'll use heat pads to make it more stable, similar to what AMD did. Or try to find Coppermine-T, Tualatin seemed like the better choice, IHS plate with bonus efficiency and performance

..aand Coppermine-T 1GHz comes with 133MHz FSB, so I'd get slower CPU at 100MHz compared to current. Or overclock AGP, 440BX can only divide by 2/3. Pick your poison 🤣

Thanks for the information!