Why do flight control cables not slacken during the cold temperatures at cruise?
If you look closely at your drawing you will see the cables are not really simple pull cables but really act like steel belts. That is, there is a pulley at each end and when you actuate the control the cable is rotated around the system in a loop.

The end pulleys and or idler pulleys are spring loaded to maintain a predefined tension on the cables and should take up any slack in the system caused by operation, temperature, or aging of the cable.



If the top left pulley above is the yoke in the cockpit, and you turn it, the top cable rotates around the loop, like a belt, and turns the actuator bottom right. Note that also means when you turn the yoke, it does not pull significantly on the springs, the cable just rotates.

Interestingly, the Concorde had to handle both contraction and expansion. When cruising at supersonic speeds the aircraft stretched up to about ten inches.

ADDITION:

For non looped cables, and occasionally for looped cables where the cable needs to traverse between objects that move relative to one another, cable housings are also used.



You are probably familiar with these on bicycles. The trick to them is the ends of the housing are attached, or anchored, to the frame somewhere. The housing is flexible so can be arranged in a loop or s-shape that can be extended or compressed as the fixed end points move relative to one another. 

The control cable on the other hand always has a fixed length within the housing despite the change in the end positions. 

The issue with these though is friction is high compared to pulleys, the inside of the housing can become contaminated with dirt and debris, and it is impossible to inspect the cable within the housing.

As with the looped system, a spring is still required, usually at the business end, to pull back on the cable. In the single cable case, actuating the cable from the control end also involves pulling on the spring.