dead summer time

Hi there,
please, what's meant by dead summer time in this sentence (Mark Twain, 'Life On The Mississippi', Frescoes From The Past)?

They have found a fragment of a lumber raft (it is high water and dead summer time), and are floating down the river by night, and hiding in the willows by day, - bound for Cairo,- whence the negro will seek freedom in the heart of the free States.

I much appreciate your help. Thanks in advance:)
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