The valence band of an insulator is completely full. The electrons in this band are a bit like guests at a very overcrowded party.
They cannot move, no matter how hot it gets, because they are trapped by the other guests squeezed up against them. You probably know how this feels: you want to cross the room to get a drink or meet someone, but you can't move because of all the people!
In an insulating material the band gap energy is very large compared with the typical thermal energy available per particle. As a
result, none of the electrons in the valence band can get enough energy to reach the conduction band.
The conduction band is completely empty. So even if an electric field is applied there are no electrons to move and so no
conduction can take place.
The valence electrons cannot move because the valance band is packed tight, so the insulator refuses to let any electrons move when
we apply an electric field. The result - no current.
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