Heat capacity

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If the heat capacity of a material is really high, does that mean it is a good insulator? (since the temperature of the solution inside changes very little)
Being an insulator means that it does not transmit heat quickly. Having a high heat capacity means that it absorbs a large amount of heat for a small change in temperature. I'm not sure if there is a general connection between the two concepts but they are definitely not the same.
 
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