Why does temperature affect cell potential?
Depending on how you write the Nernst equation the temperature might increase or decrease the potential of the cell. This depends more on the reaction quotient than on anything else.

The temperature comes in to the equation as a scaling factor where RT/nF has units Volt. This essentially defines how much the voltage changes per a decade change in the reaction quotient.

The temperature dependence here is just a matter of the scaling factor. 

Going back to the collision model, that is more about kinetics than thermodynamics and it is not at play for the Nernst equation.

Nernst equation describes the thermodynamics of the electrochemical system.

The temperature dependence can be explained by the temperature dependence of work-functions. 

Any electrochemical reaction by definition is an electron transfer. The electron goes from the highest occupied MO of one species to the lowest unoccupied MO of the other. Both these levels are temperature dependent.