The full on TT helmet is likely worth about 4 watts, compared to an aero road helmet. Over an Olympic distance bike segment, 40km, that translates to around 30 seconds. ( which will vary with the power and speed you’re already working with).
30 seconds can mean moving up or down a number of places.
Given that you’re buying a new helmet either way, and that modern tt helmets do a decent job cooling, I would definitely go with the full tt helmet.
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You could fall off a cliff and die.
You could get lost and die.
You could hit a tree and die.
OR YOU COULD STAY HOME AND FALL OFF THE COUCH AND DIE.