Yes, the tension in a spring may go up when it is cold, but it also depends on a few other things.
A spring will have tension in it if it is being pulled on on its
sides -- if it is just sitting on a workbench, it will have no tension
in it and its length will be its "relaxed" length. This relaxed length
will be (typically) shorter when the spring is cold because things
usually contract when cooled and expand when warmed. If you pull on the
spring, it will get longer, and the tension is related to the
difference between the relaxed length of the spring and the actual
length of the spring while it is being pulled on.
So, if you hold a spring between two fixed posts that put the
spring in tension, then the tension should rise in the spring as it
gets colder (the posts shouldn't get closer together as they get
colder, too, however).
This is a common feature in engineering. Most objects have some
springiness to them. Telephone wires hanging from poles typically have
more tension in them in the wintertime because they are shorter, but
the poles are the same distance apart (these aren't really springs, but
the tension rises for the same reason). Bridges too must have movable
sections so that when the road surface contracts in the winter cold,
the tension in the concrete doesn't get so high as to crack it
(concrete has a very high strength in compression but breaks much more
easily under tension).
Cooling a material also may change its spring constant. Most
materials get more rigid when cold, and this can make the spring
require more force to stretch when cold than when warm. Some materials
become very brittle in the cold and may break when stretched when very
cold (many Van demos involve immersing normally flexible objects in
liquid nitrogen, after which they may be shattered like glass). A metal
spring when very cold may fatigue easily and develop lots of little
cracks in it, changing both its relaxed length and its spring constant.
One peculiarity that you may find interesting is that rubber bands
behave oppositely to most other springs. As they cool, they lengthen a
(published on 10/22/2007)