The key to any soldering is the flux you use to clean the area. I do stained glass work and I have fixed many radiator and heater core leaks. You need to drain the radiator (or remove a heater core). IF full of coolant, you likely won't get the area clean and the coolant takes the heat away. Now back to the flux. I noticed in radiator shops they use a liquid flux they apply with a brush which is the same thing used in stained glass work. I have successfully used my liquid flux bought at the stained glass store on brass radiators and heater cores. If you are not a seasoned user of solder, don't use a flame but an iron or gun with a LARGE head to transfer heat to the area after cleaning with a wire brush and painting on some flux, it will sizzle and do its job, then put some strong solder (50/50) on the area and it should flow nicely and not bead up.
Not rocket science. If it is a big area that needs resoldering, a shop is the best bet because they can immerse the radiator except for the area needed without fear of heat going where you don't want. My 2 cents.