Heat transfer to adjacent solder joints
Not really, the key is to be directed in the application of heat to the required joint, Almost certainly you will melt the solder on the adjacent joint, however the solder should re-set quick enough. Bigger concern is to make sure you don't apply too much pressure to the fixture and dislodge the loose joint (at heat) -- 

Remember, the solder should not be contaminated and should re-set well enough.. the nice thing is that its pretty easy to test (i.e when you turn the tap back on)  - If you are concerned, or there is a leak, you can simply add more heat and apply some solder with new flux.