Question

If heat is the random kinetic energy of jiggling particles, in what way is it different to temperature?

Answer 1

The answer for which you're probably looking is that the crudely speaking temperature is intensive and heat is extensive, i.e. temperature is heat energy per molecule.

To someone who studies these things in depth, that statement is unbearably sloppy, but it gets at the heart of what you really mean.

Answer 2

Thank you for mustering the courage to be non-rigourous. Thanks!