Definitely NOT icing.
Very hot day.
35deg C
Very heavy load (7pob).
Almost 3550lb vs 3300lb certified max
Low time pilot.
5 kt tailwind on T/O
Possible fuel problem...
The current US Federal Aviation Administration approved Supplemental Type Certificate SA2123NM supplemental operational documentation relating to usage of the auxiliary fuel pump in the Cessna U206 is ambiguous regarding the operation of the pump for takeoff. That ambiguity could result in the inappropriate use of the pump and subsequent engine operational issues.
Notice the pic on page 28 of the PDF report.
See anything missing?