At low temperatures you don't produce much radiation but it is primarily Slow radiation.
All you have shown here is how controll rods work. Controll rod insertion reduces the amount of radiation produced as well as power generated. You didnt proof that temperature has an effect on radiation at all. Only that fuel rods need slow radiation for the most benefit. Keyword most. As checker does not beat dotted.
Radiation produced is dependant on core temperature.
So where do you get this? I see no proof of this. And did you take a look at this:
Compare this 4 rods huge reactor to this 4 rod small reactor.
Just for fun and gigles, set both to 51% rod insertion. Can you explain why the lower temperature reactor is better?