two different temperatures

[Nourissa]

can we create two temperatures one for the adsorbent and another different temperature for the adsorbate?

[SierraEcho]

If you are using MC, the temperature is used to calculate the acceptance ratio. For example, the concept of temperature/velocity can not be extracted from MC as the trajectories don't follow physical laws (actually, there is no physical meaningful trajectory at all).

If your fluid-wall interaction is not temperature dependent an the adsorbent itself is rigid, changing the temperature of the adsorbent shouldn't even make a different for the result of your adsorbate.

Open for a fruitful discussion about that :)

[David Dubbeldam]

In equilibrium, adsorbates and adsorbents in a single system have the same temperature.
In state-state, systems with temperature gradients are used for example to compute thermal conductivity.