I have never left Gear Down "because the brakes are hot"... The Airbus SOPs we work to are (as above) <300C Fans Off for Takeoff. If they are at 290C we can takeoff, and no issues that I am aware of with retracting gear as usual.
A340/A320/B757 all have procedure with brake deactivated to leave gear down for ~2 mins so wheel spins down (since automatic brake applicaiton on retraction disabled).
I trust anybody "deciding to leave the gear down after takeoff because the brakes are hot" makes the appropriate performance correction i.e. limits MTOW etc. since the climb gradient is based on gear up, whereas you have now decided to go gear down...
