Take a look at this link.
7. After all the thinking hats have had their say, the blue hat continues to transition between the hats in a logical order. It may, for instance, ask the red hat for its intuitive insights about the green hat’s ideas. Or, it may ask the white hat to gather more facts and information about the dangers that the black hat brought to light. After which, it may ask the yellow hat to bring forth some logical solutions to the problem at hand.
Can I summarize the above in the following way:
When all of the hats are done with giving their opinions, it is again blue hat's turn to invite cross-talks between various hat-pairs.