You don't need to refrigerate it in between.
If it's food safety you're concerned about, then chilling it for a few hours won't make any difference whatsoever to bacterial growth etc. In any case, the chicken won't probably even get fully chilled by the time you need to take it out again.
If it's food quality (texture, taste, etc.) that you're worried about, then whether you keep it warm or chill & re-heat, it'll be pretty dry and horrible by the time you come to eat it. :-(
Either way, your best bet really is to eat it as soon as poss, but if that's not an option then by all means go ahead and do just what you've described.