You can add the new file on the D drive, you have allocation contention, not IO contention (unless there are additional problems you haven't mentioned.

If TempDB is growing to 1.5 GB from a start of 8MB it should be set to start at at least 1.5GB. Add the second file at say 800 MB and set the first file to an initial size of 800 MB as well. Maybe 900 or 1000 each depending how much spare room you want. They need to be the same size and there's no good reason to force TempDb to grow from 8MB to 1.5GB every time SQL starts, unless you want to add more overhead to the apps that is. Once you've added the second file, restart SQL to reset the existing file to the new size and to clear TempDB.