"I immediately shut down the PC and pulled the heatsink off. Then I felt the CPU and it was not even warm and thermal paste looked even."
that is not a good idea, probably now you need to apply some more thermal paste
about the fan, does the video card have a fan or just a big heatsink? if it has a fan, then one fan taking air out is probably enough, if not, well if possible i would put a fan putting air in, preferably near the video card and chipset, depends on the case
"Usually around 47 if I leave it sit." and "Nothing in the case is hot, they are barely warm."
under load, if it reaches 60, you are ok, no need to worry, i would be worried when it reaches 70+ and system around 60
you say that your psu is 550w, any brand in specific or a elcheapo brand? if it is a good brand, this is enough, if it is elcheapo, you have a 300w psu there, just on the limit
"You know, since you pointed out temp1 is CPU1, I wonder if temp 2 and 3 are cpu2, and cpu3. The FX-6300 has three physical cores w/ 2 logical per physical core, which make up the 6."
each core doesn't have a sensor that the system will read, or at least i haven't meet a cpu reporting temperature to the os this way
amd never had real threads or logical cores, so it has six real cores, each core running as a thread, not 3 cores doing hypretreading like intel, you have six real cores there
temp1 is cpu probably, temp2 is chipset, northbridge or something similar, the other is southbridge or similar chip, chipset that deserves a sensor but it could be just one chipset and system sees the value twice, i had this problem in the past with lmsensors, that is why i stopped using it
"I feel safe looking at Temp1, Temp2, and Temp3. Do you think that is it and its reading each core?"
your cpu has six cores, if system is reading six values, i don't see the other 3, no, i don't think temp2 and 3 are cpu values
cpu does read temperatures ofr each core individually, so it can overclock, give a little boost to some cores when required(around 400 to 600mhz) but this measure is internal of the cpu, not shared to the os afik so you can't see the value of each one of the 6 cores, only a general value of the cpu
if you put real load on the system for at least 2 hours and then you turn off the pc and verify by hand cpu heatsink and mainboard chipset and you find temperatures closer to the temperature of your hand and bios reports similar values, forget the reports of lmsensors, they are wrong