If your child wakes up several times per night, try to measure your temperature after the longest stretch of sleep that you usually get, regardless of which hour that'll be at. If you've had an especially rough night, then mark the temperature as a 'deviating temp.' the next morning to avoid adding an incorrect measurement. Always measure before you get out of bed.
It is also good to combine your temperature measurements with LH tests if you have a big variation in your temperatures. You can purchase LH tests here.
What you can do if the thermometer beep disturbs the family:
Turn off the thermometer instantly after the first beep as you can check the value later or whenever you're up.