Without actually testing it myself or any knowledge, I will just proffer from reading the descriptions and assuming they are correct that the Ring of Pure Thought should overrule the Ring of Temptation. The Ring of Pure Thought prevents such dreams, the Ring of Temptations doubles their appearance. It would make sense that something that stopped (rather than reduced the occurrence) of something, would work in spite of something's proc rate being halved, doubled, or even tripled.
That's just assuming the coding and mechanics follow the wording and description of their effects. It could actually work entirely differently.