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Temperature of iron and wood

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If I put an iron of 350K and a wood of 300K in contact, then put them in a container so that they are adiabatic. The question : after a very long time will they become thermal equilibrium? same temperature?
My guess : they should be same. But they have different specific heat capacities. If the specific heat capacity of wood is larger . Then in order to achieve same temperature, a lot of heat will flow to the wood.
(a bit not logic) when they are in thermal equilibrium mean that they have same temperature but the heat energy of wood is higher then iron?

Thank you

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