A warm room definately helps. I carefully use a heat gun on it's low setting to warm up larger surfaces, I didn't find a hair dryer to be fast enough. What you will first want to do is size the surfaces on the ribs, particularly the blocks because the end grain soaks up alot of the water in the glue. If you've already tried a few times to glue the top on I guess you have inadvertantly done this, which is fine.
There are other methods than the 'all at once' one, which is the only way I seem to like doing it. One way is to simply clamp the top on then remove a few clamps at a time and use a thin spatula or palette knife to insert glue into the joint, another is to apply glue to the areas and let it set, clamp the top lightly then go around with heat/steam re-activating the glue and tightening the clamps correspondingly.
When I do the 'all at once' method I use more glue to re-activate any areas that set to quick, by brushing it into the joint. I tried hot water but that just diluted the glue and washed it away. Clean up excess glue with warm water. I used a 1:1.75 or 1:2 glue to water mix for gluing on the top, which is supposed to be easy to remove for future repairs. I also planned out the application of the glue to correspond with the important areas of the joint: Lining surfaces of the upper & lower bouts got glue first, then the c-bouts, then the corner blocks, then the neck block and finally the tailblock. My reasoning in doing this is to have the freshest glue on the important parts so they glue up fine with the initial clamping, and it's just the lining areas that may need extra attention. I shouldn't have to tell you to have all your clamps laid out a ready to go while you are doing this...mine are actually numbered for a particular order.