HttpCookie Is Not Deleted When Session Changes Or Is Invalid?

I'm creating an HttpCookie, setting only the name and value and not the expires property, then adding it to the response. Simple enough. The cookie is created (but not persisted) as expected. The problem is when the session changes for some reason (like the website was rebuilt, or I rebuilt my app when debugging) then the cookie stays around. I want the cookie to be valid for only the original session it was created on.

According to MSDN it says: "If you do not specify an expiration limit for the cookie, the cookie is not persisted to the client computer and it expires when the user session expires." I guess I don't know exactly what "session expires" encompasses. I figure the cookie gets deleted after 20 min when the session expires. But should the cookie get deleted if the session it was created on doesn't exist anymore for any number of reasons? The only time I've seen the cookie get deleted is when the user closes all browser windows and opens a new one.

If this is all true, I may have to store the original session id ("ASP.NET_SessionId") in the cookie, then check it against the current session id, if they're different, then delete the cookie or create a new one.

Here's the code (the only difference between my cookie and the one in the MSDN examples is I'm storing multiple values in the cookie):

private void SaveValuesToCookie(string[] names, string[] values)
{
HttpCookie cookie = new HttpCookie("MyCookie");
for (int i = 0; i < names.Length; i++)
{
string name = names[i];
cookie.Values[name] = values[i];
}
Response.Cookies.Add(cookie);
}
private string GetValueFromCookie(string name)
{
HttpCookie cookie = Request.Cookies["MyCookie"];
if (cookie == null)
return null;
return cookie.Values[name];
}