Traditionally philosophical literature recognizes a distinction between fatalism and causal determinism. Causal determinists don't say that human actions and thoughts don't or can't affect the future, just that those actions and thoughts are themselves causally dependent on prior conditions and the laws of nature. Fatalism is generally defined as something like "no matter what you think or do the future cannot be altered. It's Oedipus killing his father despite doing everything he can to avoid it.

The psychological and physical answers above sound to me like what it would be like if fatalism were true than if hard determinism were true. I mean, hard determinists think we don't have free will; it would be odd if they thought not having free will involved novel psychological or physical experiences.

Anyway, I think the only kind of free will that makes sense is compatiblist free will. So when it comes to what it would be like not to have free will I'm concerned with what it would be like if my decisions weren't made according to my wishes and reasons.

I would expect to have a very hard time predicting my behavior or explaining it after the fact with any kind of rational model. If I did have reasons and preferences to back up my decisions they would probably be invented after the decision had been made. Post-facto rationalizations instead of genuine reflection about the decision. Also, I would probably feel like I had a lot of reasons and preferences that contradicted each other and would often find myself doing x even though I wanted to want to not do x.

Rest assured, I have never experienced any of that.