If what you mentioned applies to both cases (desertion), which means that he does not care about his daughter, and gives her the freedom to do what ever she wants to do, then for S. Sistani, she still needs to take his permission, but on mandatory precaution basis, where she can refer to another marjee taqleed who allows such marriage.
In this case, she can refer to S. Hakeem, provided that the muta contract is based on no intercourse.