A casual bystander might offer a few more suggestions, especially is he/she were an interjecting type: every search is different. What kind of search are we talking about? One that only turns up a few results or one that returns thousands? What about keyword length? And what if the server needs to do extra work to parse out returns for a .PDF page, or some other special result? What about the one-shot "Lucky" search option?
The point is that the specific median of this debate over a "simple search" is hard to define, even if we restrict our measurements to just the server side. One reason is because it's hard to estimate how a server works in response to any client activity. Another is that the search itself is a varying element.
But these recent differences of statement have given us some handy benchmarks to work with to define how much energy our computers actually use, and to illuminate the server side costs of client activities in general.