Will bad conductors of heat expand faster than good conductors of heat ? or vice - versa? why so?

when some thing is heated its molecules start vibrating by gain of energy. Now if the energy is transferred in between molecules  it is good conductor of heat. it will heat up quickly and cool also. because of transfer of energy.

In case of bad conductor of heat , the energy is trapped in between molecules so it remains hotter for a longer time.

Anything when get heated it expands. so good and bad conductors both get heated and expand. But good conductors cools quickly so it returns to its original position than bad conductors.  While bad conductors remain heated for longer time hence expand also for long time.It is not necessary that it will expand faster but it will expand for longer time.