Given a binary min-heap, find the $k$-th element
The minimum element will the root. So in constant time you can find the minimum element. Delete the minimum element from the root. Now min-heapify (make it minheap) the resultant tree.
The second minimum element will be the root again. Repeat the procedure mentioned above.
By this procedure, you will find $k$-th minimum element in time $O(k \log n)$ where $n$ is the number of elements in the given min-heap.