Cold Heat soldering iron still heats up. And yes they are hard to use. Try tinning the iron before soldering and see if you have any better luck with it. But as far as soldering batteries with it, it's not hot enough and it's temp recovery time sucks as well.
Temperature recovery time is where the iron temp is at one temperature (typically hot enough to solder with) but when you apply it to the joint being soldered the heat sinks to the joint and the tip temperature drops below the melting point of the solder and then rises back up to where it needs to be, this is the recovery time. On a hot iron (40 or better watts) unless you are trying to solder 2 gauge wire or something, the tip temp never falls below the melting point of the solder.
Point I am trying to make is this. You can either fiddle around with some iron you bought from ratshack (they don't have the good Ungar any more) or you can buy good irons from Mouser, or even eBay and have the right stuff. I have 12 or so irons. They range from a 15 watt Ungar that I use for surface mount repairs, all the way out to a 400 watt iron that is made to sweat copper water line (I use it for things like 2 gauge and heaver battery feeders, radiator repair and soldering ground straps to chassis bodies) Think of it like a screw driver. The little screws will not come out any better with a large number 3 driver than a number 3 screw will come out with a 00 micro screw driver.
BUY T HE RIGHT TOOL FOR THE JOB, the added cost will save time, headaches and screwed up projects because you didn't try hack at it trying to get a result.