Is the Temperature Distribution in Molecular Simulation Uniform?

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In molecular simulation, the two sides (X direction) of the simulating system has fixed temperature 300 k. The middle area is free to any constraint. Then we add a electrical field to the system along X direction. After some time steps,the temperature distribution along X direction looks like gauss distribution. The problem is,im my opinion,the temperature is supposed to distributed uniformly. Otherwise,we may need to make the wire we use smaller on two ends and bigger in the middle?
Anyway,can anybody explain the results?
 
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How can you have a uniform gradient when both ends are fixed at the same temperature?
 
By saying uniformly distributed, I mean the temperature in the middle area (free to MD run) is supposed to distributed uniformly. If u think it has to be guass type,why do u think so?
 

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