It’s not going to be significantly greater than 3.5, and the repeatability and reproducibility of the ASTM procedure can vary the result about 0.1 to 0.2. Solarent discussed that once on here. If you’re trying to fine-tune your HT/HS by 0.2 then I’d suggest using a higher grade or an oil that reports a higher value.
The minimum required HTHS to meet the API spec for a 0W, 5W, or 10W40 is 3.5. For a 15W40 and thicker, it is 3.7.
If you're looking for a 0W40 with a high HTHS, Mobil Delvac 1 ESP 0W40 has an HTHS of 4.1. It's a dual use gasoline/diesel oil with an SN rating. If it's for a GDI engine, an oil with an SP rating might be more appropriate though.