Yes, Christians have a will. Unless God steps in that will, will run to temptation. "Lead us not into temptation." Isn't that the prayer all Christians should pray? We don't make a "decision" as to whether we want to think evil thoughts.
We exercise several choices here. What to do with that thought, any thought - whether to pursue or drop it. And we choose what habits we practice and develop. We choose where we focus our attention - whether it is on our own thoughts or toward God. We choose, in varying degrees what we are surrounded with and what we feed our senses - whether it is true beauty, good sounds and sights, etc. These choices in turn affect what thoughts arise.
The choices we make are exercises of conscience, which is formed over time and properly formed becomes integrity, the Christian goal of becoming that which we were created to be. And our conscience comes ultimately from God.