What about suppressing a thought?

I understand how we feel an emotion and the process behind that but what about a thought. I have an ex partner and on occasion I have periods when I constantly think about him over and over. I have gone through the model

C. Our relationship
T. I hate myself for still thinking about him
F. Frustrated
A. Sometimes look at pictures of us and him, or him and his new partner. Definitely think of or dream up scenarios
R: Inaction and over frustration

C. Our relationship
T. He is that guy I dated a while ago
F. Carefree
A. Go on to think the next thought
R. The thought is floating. I do not dwell.

So if I think the thought ‘he is that guy I dated a while ago’ it feels good and right but there is an element and an area that I feel suppressed and I am wondering if i will always have to suppress the unintentional thought to think of something I would rather?

Thank you x