Period Tracker is not the same as FF, it doesn't analyze input data like OPKs, CM and cervix position, and temps in order to pinpoint when you ovulate. All it does is estimate when your next period is due based on your past three month average. This is fine if your cycles are 'average' and you ovulate right in the middle like the textbooks say, but most women aren't like that.
Also, I've read how lots of women on The Bump are on shift work and manage to temp successfully, as long as you have three hours of sleep your temp should be reasonably accurate. BBT means your temp after you sleep for several hours, it doesn't necessarily have to be at the exact time every day, your body will get to its basal temperature after several hours of sleep no matter when in the day that sleep is. I know for myself, I'm an insomniac, I wake up at random times most nights and just can't get back to sleep for hours sometimes. I sometimes take my temp at the wrong time, but as long as it's after my longest period of sleep it still seems to be accurate. In fact I was away this weekend 'sleeping' in a crappy hotel bed (read not sleeping well at all), but still managed to temp after a few hours of sleep and catch my temp shift after ovulation last Thursday.
Basically, if you're serious about figuring out your cycle, you should temp. Give it a try, how could it hurt?