You will find that you can indeed use both at the same time. Switch the alarm to on prior to running the VI, make sure your temperature it out of range, then observe that you can trigger the temperature LED exactly once while the alarm is functioning. After this point the temperature loop has terminated. It will not work again.
You cannot set the alarm after starting the VI with it off because the loop in which you read that control ends after just one False read. Likewise, you cannot trigger the LED more than once because the loop ends as soon as the temperature is in range.
I suspect that you believe that only one works at the same time because you are using the Run Continuously button. That button is a trap for newbies. You should very rarely use that and only for debugging purposes. It will not restart your application until the entire VI completes, so if you have the alarm on then its loop does not end and the temperature loop never restarts... but restarting the temperature loop is not the way to keep the monitoring working. (A different subject, but you should also not rely on the abort button to stop your program. That's basically the equivalent to killing it from the task manager; only to be done if it has stopped working properly.)
If you structure your code into parallel loops like this then you need those loops to stay alive throughout the lifetime of your program and some way of communicating between loops to stop them. See attached for a rudimentary example that triggers a notification when the panel user clicks the Close button. (Also watch out for greedy loops. You have nothing constraining the speed of your temperature monitoring loop and it consumes a ton of CPU cycles while active.)
Otherwise, you need to structure all of your functionality into a single top level loop. That's certainly possible, but would take a bit longer to do properly, so I leave that to you if you wish to pursue it.
