Sorry to see this has become contentious. I'm also sorry I'm not at home, where I have a couple of good little books on heat treating for model makers and engineers at the model shop level (small scale). They would be about right to recommend, but I read them so long ago the titles elude my memory.
Cold rolling steel does work harden the surface of the metal, and the stresses this sets up do distort the metal over time if you don't anneal it before machining it. Don't ask how I know? The bottom line is you can't make carefully fitted parts from it unless you anneal it first. It is strong enough that you can make things like wear-resistant pins from it if you case harden them afterward. Then you get a hard surface, but a malleable core to resist shock.
Hot rolled is usually sold as weldable steel because it doesn't pull and distort as badly (because it doesn't have those surface stresses) much when you put the parts together. I usually use it for things like match sight hoods for the Garand and M1A. Items where hardness and toughness aren't at all critical.
As to the numbered steels, a great web resource is
matweb.com. It will give you a full of the properties of the materials in many instances, and even if you don't understand them all, you can do some comparing there.
It is worth mentioning that water-hardening steel is usually quenched in 9% brine solution rather than plain water. This reduces the chances of surface cracking. Nonetheless, the high stresses in quenched water-hardening steel usually distort it some and you have to play games with it sometimes to remedy that.
Whether water or oil hardening steel is used, after quenching it needs to be tempered or the stresses can start cracks. Just-quenched steel is called "dead hard". The worse case is the higher stress brine-quenched steel which can start cracking in as little a couple of hours in some shapes. It is not unheard of for someone to quench it then forget and leave it sitting for a few days, only to go back and find some shattered pieces in place of the part.
To keep dead hard steel from self-destructing, you have to relieve some of the most extreme stress. That is what tempering does. The term comes from the word "temperature". It means to raise the temperature of dead hard steel until it looses a certain amount of stress. The extreme hardness out of the quench is then said to be tempered. It is how that word has come to be used to mean "mitigated" or made less extreme.
With the exclusion of the 500 to 700 degree range, where, perversely, common carbon steel can become more brittle rather than less, it is generally the case that the greater the temperature is that you expose the steel to, the less hard it becomes and the tougher it becomes. Toughness is determined by impact testing. Hammer heads, for example need to be hard enough that striking nail heads doesn't batter or distort them, yet tough enough not to break. That combination tends to occur at around a Rockwell C scale hardness of 50. While the exact temperature a quenched steel needs to be raised to in order to temper it (also called drawing the steel back form dead hard) to RC-50, for most carbon steels it is in the vicinity of 800-850 degrees or so.
Thus, to heat treat a batch of hammer heads, a typical process might look like this: heat them to the quenching temperature, which might be 1500 degrees for the alloy (but is reduced as the carbon content increases). You hold it at that temperature in the oven for an hour per inch of thickness of the steel to let the heat "soak" into the steel. With professional equipment this is done in a hydrogen atmosphere both to speed up the transfer of heat to allow a shorter soak time (say, half an hour per inch) and to avoid heavy oxidation of the steel surface (slag). The steel is then quenched, leaving it dead hard and under great molecular stress. It is then taken dead hard from the quench and placed in another oven and the temperature is raised to 800-850 degrees, and again the steel is allowed to soak at that temperature for the same amount of time the pre-quench heating required. It is then cooled again.
If, instead of hammer heads, you had wanted to leave enough stress in the steel for it to act as a spring, the drawing temperature might be more like 450 degrees. If you wanted enough left to make a cutting tool, like a D-reamer, it might be as low as 300. Again, it depends on the steel composition and the manufacturers of drill rod and tool steel stock will provide a quench temperature and a list of temperatures for drawing to different Rockwell C scale hardness numbers.
I've provided a copy of MSC's catalog page with general quenching temperature and temper information on common drill rod and steel flat stock. Also something on the 500 degree embrittlement range.