Hi Gilligan! Thank you for your suggestion, I am now trying the WP Widget Cache plugin, and it seems very good. Of course this plugin is "only" caching my widgets, so now I'm not caching the main content of my pages. Surely this is way better than not caching anything at all (like I currently was doing), but if possible I would like to also cache my pages.
Is there some way I can use W3TC (or another cache plugin for that sake) without caching my widgets? In that case this would be a perfect combination with the WP Widget Cache plugin.