What is the best way to attach TMP36 sensor to the copper coil?
If you don't have to worry about conductivity from the electrical standpoint, you could use a thermal epoxy such as Arctic Silver which uses "microfine" particles of silver to conduct heat. It's a two part (redundant when using the term epoxy, I think) adhesive that is engineered to transfer heat, but may also short conductors. I've used the stuff and unless subject to intentional separating force, it holds well.