Yes an AA battery will gain (using Einstein) something like 0,000000001 gram
So, what about a foton ?
Mass = zero and speed is C Using Einstein again shows e=zero as well.
Still You can feel the impact when a foton hits you.
Is it heavy ? Can´t be ? or..
When you heat something with help of the foton then heat can´t gain anything as the m=zero
Think a foton is very strange. It is really nothing until you catch it !