Capacitors are temperature sensitive and the electronics on the NSX have known issues with ageing capacitors. You may be suffering from ageing capacitors in the cancellation control unit which are going way out of spec when the temperature is high. If you are feeling brave, you could remove the unit and open it up to see if you have any of the tell-tale signs of failing capacitors such as leaking electrolyte or bulged aluminum cans.
Use the search function to check for failing capacitors or leaking capacitors or capacitor replacement and you should find numerous threads discussing the topic. I don't think the turn signal cancellation unit has come up in the discussion - yet. But, I don't know why it should be immune (unless it doesn't have any electrolytic capacitors in it).
Failed solder joints can also be temperature sensitive, opening up as the temperature increases leading to non operation. The function is restored when things cool down. Again, only opening up the module and checking the solder connections with a magnifying glass will determine whether there are any fractures.
