Indeed:

386, introduced 1985:

http://www.cpu-world.com/CPUs/80386/Intel-A80386-16.html

Typical/Maximum power dissipation: 1.85 Watt / 2.3 Watt

And even no Pentium III 1999-2003 needed more than around 30 W:

https://en.wikipedia.org/wiki/List_of_Intel_Pentium_III_micr...

The Pentium II was not as efficient as the III. I remember setting up a dual socket machine where the PS started to matter. The best thing was that the web browser would only suck 100% from one processor.