You don't need to store 10^18 of anything.
You only need sufficient memory to store all of the objects
in your univers (which could be large, but not as large as
the universe itself).
Instead of defining a temperature across your univers you need
to locate heat sources within the universe and calculate temp.
at any location via some radiant heat function (incorporating
heat absorption by other objects).
Each object has a place in the univers, rather than each place
in the univers has an object.
Physical charateristics are functions of the objects present.