2012 13" Macbook Pro (nominal 2.5 Ghz) runs constantly at 2.9 Ghz This may be an odd complaint, that the computer runs too FAST. But, I'm puzzled and wonder what is going on.

It's late 2012 MBP 13" retina (Norwegian keyboard, not that that should matter). My son-in-law noticed that the machine runs a bit warm (80 C all the time) and the battery life is not that good.

I installed the Intel Power Gadget and found that the machine is running all the time(!) at 2.9 Ghz, independent of load or programs running.

Activity monitor shows no significant load on the machine; in fact, I quit everything else (except Intel Power Gadget), and the only load worth mention is from IPG and AM, about 3%.

I've reset the SMC, replaced the battery (not trivial, but it needed a new one), and also refreshed the thermal paste.

I'm very puzzled. Doesn't a core i5 of 2012 vintage support speed step? The machine is running macOS 10.14.5.
The Late-2012 13" MacBook Pro Retina comes in two variants - one is a 2.5 Ghz i5 CPU, and the other is a 2.9 Ghz i7 CPU. 

If you have the 2.9 Ghz i7 variant, then this is why your machine is running at 2.9 Ghz.

The 2.5 Ghz i5 CPU supports TurboBoost which allows the CPU to boost its frequency from 2.5 Ghz up to a maximum of 3.1 Ghz. In simple terms, the boost is effective only when one of the two cores are busy, but the other is not. This occurs for example when you're really only running one, single-threaded application program.