If i offered you fame, fortune and admiration (and could back it up, and no negative legal repercussions) if you killed some truly evil people like a gang of murdering pedophiles, would you do it?

Absolutely not! I detest the death penalty and I'm no executioner. Firstly, I simply don't have it in me to harm another human being
especially as a result of a logical thought process for goodness sake, no way could I even begin to rationalise it!. Secondly to murder a "murderer" I would have to be a hypocrite. Might seem strange to someone who would enjoy killing a bad person, I simply couldn't justify committing murder on the basis that "he did it first". I don't like bad people too, but I have morals too.
A lot of murders occur due to intense and overwhelming emotion. Extreme fear, extreme anger, etc. To sit and be able to say "hey I'm going to kill this person because he killed someone first and Tefal is going to give me money" is utterly barbaric and
much much worse than someone murdering someone whilst succumbed by extreme fear or anger for example.
Another way murders occur is if they are committed by an absolute psychopath. Killing a serial killer who kills people for psychological gratification is a truly ignorant thing to do, and greedy since you're [hypothetically] offering money for it! I would have many questions and would love to spend time with one (on opposite ends of a jail cell of course.)
I have been talking about specifically murder because a "paedophilic murder" suggests an intertwining of emotion and psychopathy, and suggests chain reactions leading to other things like getting rid of evidence for example.
the people believer they are doing the right thing, and will be rewarded they are taking the sane course of action to a believer.
Are you talking about Muslims believing terrorists are doing the right thing?
Well I'm no Muslim, but I have studied, and have been bought up in the company of many and I can assure you I/they don't think terrorists are doing the right thing. If I were reading the Quran and applying it to the actions of terrorists I would say in pretty much all cases they are going to hell. But my understanding of the Quran could be purely due to my disposition - which is why some people who say the Quran is the thing that's instructing terrorists to terrorise (after reading it of course - otherwise you're plain ignorant) should perhaps put that Quran down and look at themselves in the mirror...
The fact is that they are born and raised in a country and family where Islam is the principal societal statute, this means that any action they contemplate and then try to rationalise will be channelled through Islam, because they simply don't know anything else which they can use to try to justify their actions to themselves and their peers. People need to understand how these extremist cliques come about. Justifying to peers is also important because evil people tend to gravitate toward and keep company with similarly evil people.
In most extremist's cases, violent tendencies are already manifested in a person's psyche
before the religious texts have a chance to be logically processed/understood by the brain. Imagine a person with a psyche which is predisposed to violence, murder, or even killing people who kill (just like in your hypothetical situation) living in a country where Islam is everywhere. This person will channel his violence or his desire to kill people who kill through Islam itself. They will use Islam as the justification.
You also need to remember that a lot of terrorists are converts to Islam. These people definitely will have read Islam with a predisposition to commit violence!
This is exactly what happens when a person reading Harry Potter wouldn’t root for Harry Potter. You can read exactly the same lines as the next man but your response to certain things is based on your individuality – just like some people’s response to a pedo-murderer is killing them.