For any concerns I'd contact the manufacturing company's customer service or their tech support and talk directly with them with your concerns and talk to them about safe distances for firearms. Ask about safe storage of ammo and distances for ammo from heater.
Personally I wouldn't store loaded ammo in a heated safe. If you want your ammo locked up go out and buy a cheaper safe for your ammo, primers in a seperate srorage unit and gun powder in a seperate storage unit.
As long as it is dry and at room tempeture it will last for decades. I know guys that reload out in there unheated garage and store all ofvtheir reloading stuff, loaded ammo and guns out there and it reaches over 95 degrees in the summer and in the winter the outside temps gets near zero degrees.
Needless to say the have moisture problems. The press, dies and all other bare metal surfaces will start to rust. They have constintly check stuff out and keep every thing wiped down with a oil bace lubicant.
If they had a little heat source to keep the inside of garage up to 45 -50 degrees would eliminate the moisture problem, but that would never happen.
The tens of thousands of dollars I have invested in all of my reloading equipment, firearms and accesaries are all stored in a big walk in closet, whrn it comes to this investment I wear the pants in the house. No way would I be told by the other half to store them in a uncontrolled envirorment.
For your storage arrangment having all of that loaded ammo in that heated safe would be alarming to my. Just my personal thoughts.