There is nothing bad that happens to your cpu if the temp drops below 40 deg C. In fact, if you can get it closer to 30 deg C it will probably last a little bit longer. The one thing you want to avoid though is “thermal cycling” (having the temperature go up and down and up and down, etc). Computers are made of many different materials, and they all expand and contract at different rates. These stresses caused by varying temperatures can eventually cause faults (for example, the tiny little wires that connect the silicon to the pins in the chip can eventually lift up off of their pads and disconnect, and then the chip is broke).
This is what leads to the age old “leave it on all the time” or “turn it off when not using it” debate about computers. If you leave your computer on all the time, then there is one set of effects trying to kill it (friction on moving parts like fans and disk drive motors, heat, transistors constantly switching on and off, etc). If you turn it off when you are using it, then there’s a different set of effects trying to kill it (thermal cycling being the most prominant). Oh, and by the way, even if you never turn the thing on, there’s an aging effect inside the silicon trying to kill it. You can’t win.
I personally don’t like to have any chip in my entire system running at more than 40 deg C. Coincidentally, the human pain threshold for heat is right around 40 to 45 deg C, so you don’t need any fancy measuring device. If you touch it and it makes you say “ouch” then it’s too hot and needs more cooling (what I like to call the highly scientific “ouch” test). There’s a trade off between cost and long term reliability, and since most people replace their computers every few years, it doesn’t make much sense for the manufacturers to design them for a 10 year life. Hence, many CPUs run a little hot. A rough rule of thumb is that every 10 deg C above room temperature cuts the expected life of the device in half (which is notoriously inaccurate on the low and high ends of the temperature range, so don’t worry much about the change from 30 to 40 deg C). Above 70 things go bad very quickly, which is why most computer alarms are set around there.
Find out what temperature your CPU tends to run at. If it’s more than 50 I would recommend getting some better cooling for it. Once you know what temp it runs at normally, you can set the alarms much closer to that temp.
As for the hysteresis temperature, I don’t have a system that has this feature so I can’t say for certain, but what I would expect is that the temperature alarm turns on when the temperature gets above the high temperature, but the alarm doesn’t turn off again until it gets below the low temperature. This is what Sam Stone was getting at, you don’t want it to be constantly turning on and off and on and off as the temperature fluctuates around the high mark, you want to build some hysteresis (delay) into when the alarm shuts off.