Will using await on Task.Run casue "access to disposed closure" error?

Code Sample

public async Task HeavyTask()
{
  using(var res = new BigResource())
  {
    await Task.Run(() => service.Do(res));
  }
}

I have some code that looks like above, and ReSharper warns me about "Access to disposed closure" on the use of the res instance.

If I did not use the await keyword, I know the res instance might be disposed when the service tries to access it.

But I think if I use the await keyword, the thread that executes the HeavyTask method will not continue until the Task.Run is completed, and there should be no risk of accessing a disposed closure.

Please help me understand where I went wrong, and what would be the preferred pattern to solve this problem.