I decided to turn to the PC Gaming community on Google+ with this question. As it happens this community proved very helpful and according to them 63 is nothing to worry about. The critical temperature is 74 degrees Celsius. To be on the save side we installed an additional case fan. Finally we ran a test with a Linux program called Stress. Stress is a simple workload generator and maxes out the CPU to 100%. During the test the temperature rose to 66 degrees Celsius which is, again according to the PC Gaming community, acceptable. Happy with this result we decided to stop tinkering and start gaming.
|stress running on our AMD A10-7800 with Ubuntu 14.04LTS. The CPU's are at 100% while the temperature didn't go beyond 66 degrees Celsius.|