Variacs are variable (auto)transformers, not potentiometers.
The limitation on the variac current is the output current. If it is rated at 8A you can draw 8A at 1V (8VA) or 8A at 200V (1600VA).
You can expect them to get warm during operation due to losses, like any transformer. Probably good quality ones will get less warm than less good ones, due to less copper and/or poorer electrical steel being used in the construction of the latter.
It's not uncommon for variacs to have taps for the primary, if you connect more voltage to the primary than they are designed for (or operate them at a lower frequency than they are designed for) you can get excessive heating even with no load at all.