I've had to do this effect on several of occasions, and have found several different ways of achieveing the effect (with varying degrees of ease, though usually the more difficult gives the best results.
1. In FCP, create a white solid about 10-15 frames long and place it above where you want the transition to happen. With the Pen tool, rubber band the opacity so that it starts at 0%, goes up to 100%, and then back down to 0%. Then change the Composite mode of the solid to "Add". (I've used this several times when I needed a quick fix, reults will vary depending on the footage. You some times have to play with the timing to get it looking right. As a rule of thumb, I allow 2 frames of fade out for every frame of fade in.)
2. In FCP, add the 3-Way Color Corrector filter to both clips. On the first clip, go about 5 frames before the end of the clip and set a keyframe. Then go to the end and adjust the picture so that it is blown out. ( if there are a few traces of color thats ok.) then do the same with the second clip except start with it blown out and then return to normal. (the timing might need to be adjusted, just re-adjust your keyframes in the effects panel)
3. The third way (which I believe gives the best results) is by exporting the the two clips as one movie file(so that the movie is the legnth of the 2 clips with a simple cut. I then take it into After effects and put that clip into a new comp. I then add an "Adjustment layer" on top of the clip and to the AL i add the "glow" filter. I then keyframe the filter much like in the previous way where i set a keyframe a few frames before the cut. Then on the frame of the cut, i adjust the brightness, radius, and threshold so that the image is blown out, then move forward a few frames and return the steeings where the image looks normal.
These are the ways i achieve the effect. I havent tried John's idea but i liked the sound of it and i mean to give it a try.
Hope this helped.
James