It is possible to take your BBT if you work shifts, but it will be more challenging. Take your temperature at the time you wake up when you are most likely to have had the most sleep. Be as consistent as you can. On your days off, take your temperature after you wake up as well, even if it is at a different time. Make a note on your chart of changes in your waking schedule. You may take your temperature in the afternoon before you go to work if that is your usual waking time and the time after which you are most likely to have had the most sleep. It is not useful to take your temperature when you are already awake and active.
Another option which may however end up being quite expensive is to look at the newly developed wearable temperature sensors. They can monitor your temperature while you sleep. Some of them support shift work and provide more reliable temperatures than taken with a traditional thermometer in these situations.
The video chart interpretation below shows how you can still detect ovulation and your fertile time on your fertility chart while working shifts.
Video Chart Interpretation: