I would recommend you to have another class called File.
public class File
{
private string filename;
public File(string filename)
{
this.filename= filename;
}
public void download()
{
// download code using filename
}
}
And in your thread creation code, you instantiate a new file:
string filename = "my_file_name";
myFile = new File(filename);
ThreadStart threadDelegate = new ThreadStart(myFile.download);
Thread newThread = new Thread(threadDelegate);