There are no "laws" (that I'm aware of) that would prevent this, but it is walking a fine ethical line - and it's probably going to create more problems than it's worth.
The ethical concern stems from the fact that your literature work came as part of your thesis project. Your project probably was originally suggested by your tutors, you used institutional resources (i.e. the library), and you were most likely supported by the group during the process. The only way I see there not being an ethical issue is if you came to the group having already conceived of the idea and performing your literature search.
As a practical matter, if these people are as "hot-tempered" as you claim, imagine how they are going to react when they see your review in print. They have a track record in your field - you don't. They can have a strong negative effect on your professional life. Why risk turning an indifference about you into outright enmity.
Also, what is a review article going to buy you? At this stage in your career it's really just "padding your publications" and most people will recognize it as such. Reviews don't carry much weight with hiring managers/committees because they are not independent research - you haven't shown you can produce anything new and novel. (Reviews tend to be written by more experienced people because a) they can afford to waste the time (they already have tenure), and b) they have the breadth of experience to put everything in context.