firstly, dont get this wrong but creating duplicate threads is not a good idea..
secondly, i have no idea about a cache plugin, but if it's as you said due to 'heavy activity' i could offer you somethings that might work.. (by the way i wondered how such a big activity can cause this situation, could you ask them how much cpu percentage they allocate for each hosting ?)

try disabling trackbacks, prune your hitlog, disable your ping services and focus on the antispam central to prevent spam attacks, and may be order your robots.txt file..

these are some advices from me without much wisdom; that might work

CMP wrote:

My b2evolution Version: 1.10.x

My host has suggested that the easiest way to prevent my blog from overloading his server is to install a caching (or catching?) system for my site.

Would you please let me know if there are some available and which one would be the most appropriate for my b2evo version?

Are you running 1.something? If so upgrade. I actually don't have data that says it will help but it is newer/better/smarter so I assume it will. Actually given that there is a "delete pre-rendered item cache" that never existed before I'm thinking it *will* help. Otherwise it's like tilqicom suggests: prune some of the "fat" from what your blog has to do for each visitor. Extend the ideas above to include removing widgets that you might not need - especially on single post pages (something very easy to do in 2.4).

Sorry, and my apologies.

Before making second post I started looking for the first one and couldn't find it. So, since I'm not expert in forums I supposed I did something wrong and, as a result, the first one was never published.

The plugin my Host suggested is this one:
http://forums.b2evolution.net/viewtopic.php?p=25724#25724

Aren't you familiar with it? What is this good for?

The CPU percentage allocated to me site or blog is 25%. Last time this CPU problems arose it was solved by creating static pages. I ignore reason for today's.

I'll tell my tech guy about your suggestion. Thanks a lot.