You probably do feel like doing something you are tempted to do. You may also be torn - at odds with yourself - or your may be conflicted about the activity. All these things been that part of you feels like doing that, and other parts of your mind want you to not, or to do something else. If it were not for that part of your conscience or mind with a second or third idea, you night not use the term tempted at all. You would just go with "I want to." So in this way, there is a difference.

I'm tempted to = Something causes me to feel strongly disposed to (doing....)

Being tempted to do something means you know it's probably in your best interest not to do it. To feel like doing something means you simply just want to do it. For example: "I'm tempted to empty out the money that remains in that bank account and take it to a casino." You know it's not a wise decision to gamble with that money, but you know it will be fun. You're giving into temptation by gambling.

Hi Nozturk! Usually when you're talking about being tempted to do something you do kind of have to address what else is going on in the situation. Being tempted more often than not means you were not originally thinking or planning to do something, but someone or some thing started to push you to do it (whatever 'it' is). So, you don't necessarily need to think of it as something you "feel" like doing, rather something that you were not originally planning to do but ended up being influenced to do.

"I'm tempted to ....." = I want to do something, but I shouldn't do it "I feel like ...." = I want / I want to...