Brass can be annealed by heating and air cooling. The reason many think it has to be water quenched is because when annealing cartridge cases they are stood in water and knocked over after heating. This is done to prevent the heat from reaching the cartridge base which must retain the full strength of the alloy as manufactured to prevent failure. Either way will anneal the brass. Yes, working hardens it fast.
That looks like a sand cast guard and it may not take the required bend without breaking as the bend looks like it will be concentrated in one area.
That trigger guard looks like it is for a Baker rifle. If you got it from the Rifle Shoppe it should bend easily. But remove that casting sprue between the front of the trigger guard and the post in the rear first. Heat it and let it air cool like the others have stated for insurance. Brass does work harden so it needs to be softened.
Good luck on your project. Mike
You are probably going to have trouble not so much bending but making the guard not look awkward. I assume and hope your stock profile is not what you drew. I would hope you have a smooth curve to accomplish the angle and not straight lines and a hard inside corner.
When I had to deepen the bow of my trigger guard to accommodate the forward swing of a DASST I heated that area to a cherry red, and bent it while it was hot. I don't know if that was the "right" way to do it or not, but that's what I did, and it stayed together and didn't break. I did things similarly for modifying the shape of the various unsupported spurs.