Update after seeing the fixture image:
There's no need to bolt the box to the support framing other than to secure it in position. Nothing hangs from the box (so it doesn't even need to be fan-rated). I would still run the 2x10 over the box, and I'd add blocking on each side of the box to bring it down flush with the adjacent joists. This will give you solid backing for the fixture board and/or the eye screws.
| |__________________________________| |<-- joist
| |__________________________________|<-|--- backing board
light box spacer block
A 2x10 spanning just ~15" will carry that load without breaking a sweat. It's all a matter of good fastening.
I would run a 2x6 or larger, laid flat, over the box. Secure it with at least three 3" gold construction screws or two 1/4"x3" lag screws at each end. Bolt the box to it. (If the box you have now isn't fan-rated, upgrade it. You need the mounting screw holes for the fixture to be robust enough for the job.)
Heat escaping electrical boxes isn't generally a concern. If it was, all boxes would be required to have clearance or insulation. If enough heat is being generated to cause a safety issue, something's badly wrong with the wiring.
Unsolicited protip: Next time you cut a hole in drywall for repairs, leave an inch or two extending past the adjacent framing. This way you can float backing for the patch without having to fasten it to the existing framing. It's much quicker and doesn't require careful positioning.
Engineering point of interest: The chains on that fixture hold approximately twice the weight you might think. This is because of their angles. Whereas a vertical chain would hole more or less half the weight of the fixture, they now hold roughly the entire weight of it... each. Load force increases exponentially as the angle strays from vertical. If you're selecting chain yourself, be sure that it's up to the task.