Most Cessna aircraft have performance charts the range from 0 to 40 Celsius. I've had a CFI tell me that the FARs prohibit flight if the OAT exceeds 40C or whatever is shown on the performance charts. Is that a true statement? I have not found anything in Part 91 that addresses this.
Yes, it is legal, disregarding any catch-alls such as 91.13 reckless operation or ones pertaining to pre-flight planning data like takeoff distance.
It is simply left to the pilot's good judgement for a go/no go decision depending on whether or not the flight can be completed safely.
Edit: Re-reading this answer much later, I would like to emphasize, "disregarding any catch-alls".
With regard to the catch-alls such as 91.13, this could very easily be considered illegal, but no rule with a statement clearly identifying taking off with temperatures higher than those on the charts as a prohibited action exists to my knowledge. Do not do it.
It is legal, though not recommended as aircraft performance has not been fully quantified in this regime of the flight envelope. As pilot in command, you have the final authority to decide to proceed here. Keep in mind, however you could be held civilly liable should an accident occur under these conditions.