It is normal to all android phones. the Android OS consumes a lot of battery power because it performs several tasks.
Hi troy, Alec is correct. This is not just your Note 2 but almost all of high end phones have this problem. In line with this, you might want to check out my post on how you can maximize your battery life, just click the link below. I hope it'll help.
I also bought a Note 2 from Globe on June 8 and upgraded to 4.1.2. The phone was cool for a few days before and afterwards, so I can not blame the upgrade for the overheating which followed.
After a few more days the phone started to get very hot and act strange. It would turn itself off by itself for example.
After a few more days of getting hot the phone died. It would not even turn on. I would not give full faith to the advice that all Android phones run hot because mine did not run hot at first. It seems that yours did not run hot at first also. Also consider this: When my phone started to run hot it would eXhaust the battery in about 4 hours. This is NOT normal for a Note 2. I could go all day (24 hours) on a single charge. My "New" Note 2 lasted a little more than a month before it died. I have another post which is curious about whether or not the phones are new.