I'm surprised at some of the suggestions for 'any soldering iron'. I'm sure they're correct...it's just my experience buying a cheap one was horrible....it doesn't seem to get hot enough to properly melt the solder, dunno why - I have to spend ages pushing the solder in different directions until it hits the right spot and melts.
I only learnt a bit about soldering at my last job, around 2002, and because it was professional they had some quite good equipment. I'd say it's well worth your while getting one of those little contraptions for holding wires in place - it's like 2 clips on mechanical arms, that are both fixed to a block. You just use the arms to hold each piece of wire, in front of you, so they don't try and come apart etc.
I need to do some soldering of heated grips soon so I will be watching this thread for new soldering iron suggestions