Sir,
Suggest a material which is bio-compatible and having a low thermal conductivity and low diffusion rate

There are many good candidates. For example, a large variety of ceramic materials would meet the requirements you listed, such as porcelain, alumina, hydroxyapatite, zirconia, etc. These materials typically have very low heat conductivity and diffusion, are usually extremely hard and durable, and can withstand very high temperatures. However, they can also be brittle since they are not flexible. They'd be good for producing a crown for a tooth, for example, but not for making artificial skin.

There are also many synthetic and natural polymers which may meet your thermal conductivity requirements but might require further examination for their diffusion properties. Biocompatible synthetic polymers include various formulations of nylon, low-density polyethylene, silicone, polyester, polyurethane, and a wide variety of fluoropolymers including PTFE (Teflon), FEP, PFA, and ETFE. Natural candidates include collegen, carrageenan, hyaluronic acid, as well as various cellulosic polymers.