Really depends on what section you are doing.
The path ranges from the section between St Ives and Cape Cornwall
where boots are a must as It is a very uneven, rocky path through to
the section between Braunton and Bideford in North Devon which is
along an old railway and could be walked in trainers.
I have walked the whole path ( not in one go mind- it took me 12 years ! )
and consider that proper boots are best for most sections-- especially as
the best bits tend to be the toughest !
Unless , amazingly, we have an Indian Summer, the heat will not of course be
a factor
Hope this helps