Having checked the specification for the two processors, the thermal theoretical maximum is the same, so your existing heat sink should be adequate.
Assuming your motherboard supports this processor, it should be just a matter of removing the existing heat sink retainer. Gently remove the heat sink from the existing processor, not forgetting to un-clip the fan cable. This should be done by a gentle swivelling motion, just to break the bond that occurs between the heat sink and the CPU. Now raise the Zero force insertion lever 90 degrees and you can lift out the old CPU. Try not to touch any of the pins for two reasons. First the risk of static electricity and second the chance of grease from your skin getting on the pins.
Next, turn the heat sink up side down and remove all traces of the thermal compound used for thermal transfer. Do this carefully. You want as close as you can to a mirror finish. You will probably find the underside has a copper base.
Now you need to apply a quality thermal paste to the top of the CPU die (only to the die). Arctic Silver is about the best you can get and only requires a very thin layer.
Place the CPU in the socket. NOTE. NO FORCE AT ALL is required. If it doesn't just drop in, you have it around the wrong way. Look at the shape of the pins on the CPU and compare them to the socket for correct alignment. One in place, close the ZIF lever back to its original retained position.
Now place the heat sink back on top of the CPU. Again, be careful to align this properly. There may be a "step" to take care of a ridge on the socket, so correct alignment is essential and re-secure the retaining clip. DON'T FORGET to reconnect the fan NOW.
Double check all is well and you should be ready to go!