Actually, with most chips (but especially AMD CPUs), any temp readings under 40C are far from 100% accurate. But even for Intel chips, it's perfectly normal to run in the low 40s at idle & stay below 60C when operating.
As for the stock cooler...any stock cooler is going to cause problems if a) the heat sink is clogged, b) the thermal paste is incorrectly applied, c) the case doesn't have very good airflow, or d) you attempt to OC the CPU with the stock cooler. That holds true for both AMD & Intel.
I have the stock cooler on my FX-8320, but I also have the maximum case fans in my case (front, bottom & side intakes, rear & top exhaust), & my CPU stays below 60C even when gaming in BF4. So, check the heat sink, add more case fans if there's space, & for half the cost of an aftermarket cooler you'll be able to keep your temps plenty low.