This question came up today.
Our Thoughts: (one Programmer and two mechanical Engineers)
As steel gets cold, it will compact and therefore get denser.
As it heats up it expands and becomes less dense.
We think that less dense would allow for a greater bounce.
Let us assume for the experiment we would release the balls from the same height from electro-magnets like any good Physics I lab.
The Surface will be a uniformed Steel Lab table.
Which would bounce more and why?
Jim
When you say “bounce more”, do you mean, “Bounce more times before coming to a halt”, or, “Bounce higher at the initial bounce”?
I read about an actual experiment with this with regards to baseballs. Heated baseballs bounced less right out of the microwave (because the leather on the outside had softened), but after an hour or so, they bounced much higher. Chilled baseballs bounced much less.
I’m trying to think of why density would change the coefficient of restitution. I can’t think of any reason why it would off the top of my head. Provided that the heating and cooling processes didn’t cause any grain changes in the steel, I’m going to vote for c) they bounce exactly the same. But that’s just a guess.
My bet would be that it depends on the two temperatures and which is further from the temperature that results in the greatest elasticity for that material. Two cold and the ball will have zero bounce, too hot and it will just squish like a pile of red-hot, glowing poo.
I.e. there isn’t enough information in your question to be able to say.
Too cold … *
Go with Bounce Higher.
Ball #1 cooled in Freezer set to 30°F for 24 hours.
Ball #2 lets say heated in Boiling water for 15 minutes.
Ball #1 should near 30°F and Ball two should get up above 120°F
Thank you tiltypig
Baseballs are more variable, Humidity alters them quite a bit and they have uneven surfaces. We actually started with Baseballs and Basketballs and decided that Steel Balls would be a better test as far as controls.
Dag Otto: Interesting guess, maybe someone can back it up.
Jim
That’s only two pieces of information, we need three. What is the temperature at which steel is the most bouncy?
And is it a linear progression of losing bounciness as you vary from the max in either direction or an irregular curve?
Without doing the math and/or sufficient tests to determine a table of bounciness over a range of temperatures there is no way of knowing the answer. So unless you’ve got money riding on it and know a physicist with a whole lot of time to spend on the calculations…
If you could get your hands on something like this text here, you could probably start working towards an answer.
IANAPhysicist, but my WAG :
colder ball=>more rigid=>closer approximation to inelastic collision=>higher bounce (because less energy expended in deformation of ball itself)
Food for Thought: Extremely detailed testing methods.
Testing Croquet Balls
Section C. Coefficient of restitution (bounce) is important.
I need to read through it and see if it points the way.
With a steel ball, and everything else, these two are exactly tied to elasticity (bounciness). Never would one ball win one of these contests and not the other.
That’s my WAG too, and it seems to be backed up by this team at Harvard University
That’s all very interesting, but what happens when we bounce them on a treadmill ?
You had better dry off the boiled ball before you drop it.
I would think that the water would effect it somehow.
God will get you for that one. (Not to encourage you, but I did laugh out loud when I read that!)
Colder should bounce Higher and More?
Your Cite seems be saying that for Steel it wouldn’t matter.
Jim
They said for hard steel it doesn’t seem to matter, but, on the other hand:
The coefficient of restitution is a measure of the elasticity of the collision - higher CoR => more bounciness. 316 SS, M50, Armalon and 410C are all types of steels.
I refuse to get involved in the treadmill argument. 
Wait, this isn’t a treadmill question.
I think I am not understanding your answer.
Are you saying Colder = more bounce or less bounce?
Please be patient with the Physics impaired. (I am 20+ years removed from my Physics I class and I don’t really understand coefficient of restitution in English)
Sorry for the bother,
Jim
If you look at the link Sage Rat gave, the type of steel involved makes quite a bit of difference.