PreWarmCache for MVC Application with Stopwatch Infinite Loop
There are some things that you could have done better certainly.

My first pick is the class name DoStuff. Please try pick a more meaningful name like Action or Task. 

In this class you seem to be appending the current time to the property DoStuffName (which should also be renamed accordingly). You could pass the name in the constructor and append the current time instead, like:

public class Task{
   public Task(string name){
      Name = name + " " + DateTime.Now;
   }
   public string Name{
     get; private set;
   }  
}


You also seem to have one of the most evil bad practises of programming - the empty catch block. Be sure to, at least, log the exception somewhere.