Well 300'agl sounds about right for a proper base leg,
and if he had landable fields in all directions....so
that if he circled in sink on the outside of the thermal...then
in theory he might have been able to land even if he
had not centered it and could not make the runway.
I have experimented thermalling low right next to
a runway when conditions and traffic permit...and u
can burn 300' in one orbit. IMHO 600'-800'agl gives
you more leeway, take another tow if u get below that...it
is cheaper then funeral expenses.

And never thermal in the pattern without thorough knowledge
of the field and traffic procedures, and with a working
radio I would think