You guys do know that some explosions teach the temperature of the sun.
The sun emits so much energy not because of heat but because of mass- the sun is enormous....
Basically-- Amaterasu could be as hot as the sun- of Sasuke made a Amaterasu ball the size of the sun it would probably produce the same amount of energy As the sun.
I have a theory as to why Amaterasu might even be hotter than conventional fire.
So,fire emits energy as thermal and solar ( heat and light). However Amaterasu is black-it is entirely possible that instead of giving off energy via light- it only gives off energy via heat.
Nuclear bombs give off heat around the same temperature as the sun--- nuclear bombs are shown to vaporize rock formations. If bijudamas vaporize rocks via thermal energy- then they would be as hot as the sun when they explode.
If biju Damas might be as hot as the sun- then why not Amaterasu... Being as hot as the sun isnot as impressive as you think....
Mass vs heat
High temperatures are common in nature. Some lightningbolts reach 54,000 degrees -- that's hotter than the suns surface.
So, Sasuke already has a technique that is hotter than the sun ( Kirin )
Being as hot as the sun doesnot mean you emit the same amount as thermal energy as the sun.
It dopends on how long you are that hot for- and the mass of the object that is releasing thermal energy.