Does temperature affect to the movement of the electrons circulating the core of an atom? Do they move faster if temperature increases?
In most general case electrons do not circulate around the nucleus. For instance in the ground level of the Hydrogen atom electron has angular momentum equal to 0. However in more excited states (higher energy) or many-electron atoms electrons can acquire angular momentum. There however can be states with very high energy that have 0 angular momentum.
What temperature does - it excites electrons of some of the atoms into the higher states, so they in principle go to different states mentioned above.
To understand this clearly one will need to read some QM textbook or at lest wiki on Schrödinger equation for Hydrogen atom.