Subject: Quantum tunneling and violation of 2nd law of thermodynamics

If a gas in thermal equilibrium with its surroundings is contained with a 
partition whose thickness is specifically adjusted to allow only the fastest 
molecules to tunnel through, could a temperature difference spontaneously 
develop? I.e. could a passive molecular velocity selector be built based on the 
quantum tunneling effect? If so, could this not be used on a large enough scale 
to create a sort of heat engine? 

Re: Quantum tunneling and violation of 2nd law of thermodynamics