The advertised TDPs on the AMD products are accurate. Part of the reason why an APU is more efficient is because the CPU and GPU are on the same die and so close that lower power is required. Lower power = less heat. A HSF sized for a 100W APU would be similar to a HSF sized for a 100W CPU only. The thermal load is essentially 100W regardless of if it's produced by just the CPU or by the combined CPU/GPU.
I am not a Linux user but I do know that AMD has made a very Big step forward in graphic drivers for Linux as well as Windows. In fact there is a growing interest in Linux based games as they often run faster on Linux than games on Windows. The days of weak AMD graphics drivers are hopefully over with new attention being paid to them.
I tried the manual driver download and it worked for me but it may depend on what driver you're trying to download or there might be a server issue?