Yes your waking times will make a difference. It is important to try to take your temp at the same time every day. Even if you set your alarm and then go back to sleep, it should be at the same time.
I notice a change even when I get up around 8am on the weekends when I usually get up at 6am during the week. There is a temp adjuster in fertility friend. I cant remember where it is, but just look under all the tabs and you should find it. You put in your usuall waking time and the time you actually got up and the temp you got and it adjusts it for you. I personally dont think it is totally accurate but it is close.
Im not temping anymore so I dont go on FF hardly ever, just to update for af.