Sorry I can't help with the boat rental question either.
Just in case you've never done this before, you should have a look at this map from the "swiss lifeguards association" http://www.slrg.ch/uploads/media/aar..._Thun-Bern.pdf
Just after Thun there is a bit of a tricky spot (big waves/high speed depending on water volume) at the railway bridge near Uttigen station ("Thun-Bern SBB" on the map). It is marked as "very dangerous part for inexperienced boatlers(swinglish) /Schlauchbootfahrer".
It is doable, although we always have discussions if we should pass left or right.
So if you don't feel overly confident you can just take the regional train Bern-Thun (via Münsingen) to Uttigen and embark after a short walk from the station.
Here is another link to a site showing the current water levels. http://www.infosport.ch/kanu/levels/navlevel.htm
Forgot the fun part: Start early and take some drinks and food with you, so you can have a nice bbq at the banks of the river.
And if you know all this already, have fun anyway!
And here am I thinking about when to prepare my board for the coming winter..