I couldn't find anything wrong with the water supply, seacock, strainer etc., and the exhaust system seemed to be fine.
Then my partner found this post:
Solved! Overheating Yanmar 3GM30 due to Johnson raw water pump not priming.
Now, Raasay's pump is below the waterline, so priming was not really likely to be the problem (it's full of water all the time). However, the post also explains that the pump cam can wear over time (especially in silty conditions).
On many 3GM30s sold in Europe, it seems that the cam cannot be replaced - it's part of hte pump casting. However, Raasay's pump (like many sold in the US, for some reason) has a replaceable cam and I was able to source one (after some meandering) from ASAP for around £20. (I could have imported one from the US for a little more than twice that ...)
Here are some photos showing the old cam and the new one - they are a bit dramatic. I wonder, as well, whether the larger water channel openings in the new cam are an indication that the old one may also have been a replacement - and maybe not quite the right part.
Old cam in position
The new cam is on the left.
New cam in position.
I have reassembled the pump, and will be testing it the next time I visit the boat. Watch this space.