To "give way to temptation" or "give in to temptation" are the same - they mean to allow the power of temptation to affect your behavior. For example, if you are trying to stop smoking, but someone offers you a cigarette and although you know you shouldn't take it, you take it anyway, then you are giving in to temptation.
"Give way" can also refer to the collapse or crumbling of a physical object. On the other hand, "give in" usually only refers to an emotional or metaphorical collapse.
Cheers