How to unit test code that suspends its execution without abstracting it out?

I have to unit test a method that suspends its execution (does some work periodically):

void m() {
 do {
  doSomeWork();
  Thread.sleep(1000);
 } while (condition);
}

What I have to test is multiple while loop execution and check if the doSomeWork() has been done correctly. So currently my test looks like this:

1) start execution of m() in a new thread.

2) in the main thread: Thread.sleep(1000 + 200);

3) in the main thread assert that the work has been done correctly.

4) in the main thread: Thread.sleep(1000 + 200);

5) in the main thread assert that the work has been done correctly.

6) and one more time 4 and 5

The problem is that the doSomeWork() on different machines takes different amount of time and its hard to find a good value to wait in the test.

I have seen a common approach to such situation is to abstract out the sleeping time and in test code don't wait: C# Unit Testing - Thread.Sleep(x) - How to Mock the System Clock

But I really have to verify that the implementation is waiting.

Do you have any suggestions how to write a robust unit test code for such scenario? It can also involve refactoring of the m() method.