q = 0,  
ΔU = q + w 
or ΔU = 0 + w
The wall is adiabatic as no heat is absorbed. 
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is the equation correctly written ?

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ΔQ  = ΔU + W

Heat supplied = ΔQ = heat absorbed by the system
Change in internal energy = ΔU = Energy or Heat  absorbed by the system.
Work done by the system = W

   so   ΔQ = 0      =>  - ΔU = W

If no heat is absorbed by the system, then the work W done on the system increases the internal energy U of the system.  The temperature increases.  Since there is no exchange of heat between the system and the environment surroundings, the process is adiabatic and the walls of the system are totally thermally insulating.

   Work done on the system. So W is negative.  ΔU is positive.  So ΔT is positive.

The system is like an insulated piston fitted in an insulated gas cylinder and the piston is externally pushed in.  So pressure increases, volume decreases.  Temperature increases.

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