I am a fairly recent Ubuntu user and not a computer expert and I was having exactly the same problem as you. After some struggling, I managed to avoid the message "CPU Throttling apparently enabled!" and got ATLAS 3.10.2 installed.
The first tip I got in https://sourceforge.net/p/math-atlas/support-requests/859/#f11d, where it basically says that "The only time ATLAS should detect throttling that isn't occurring is when the processors are fixed to run at a lower speed than their maximum speed." My processor was not running at its maximum speed, since I had a BIOS speed limit.
If you have the same problem, look at the maximum frequency allowed in the file
/sys/devices/system/cpu/cpu0/cpufreq/scaling_max_freq. Copy this value to the files for each processor(/cpu/cpu1, /cpu/cpu2 etc). You need to do it as super-user, but before it takes effect, you have to edit the file
/sys/module/processor/parameters/ignore_ppc from 0 to 1. More details are given here.
This was still not enough for me and I figured out that I had to edit the files
/sys/devices/system/cpu/cpu0/cpufreq/scaling_min_freq to the same value that was used before. After that, I did not get the boring message any more and ATLAS was successfully installed!
update: I have just gone through this process again and it seems that the real problem is to have the power scaling driver intel p_state enabled. The procedure above will only work if you disable it first. Follow the instructions in here and replace "enable" by "disable" as explained here.