How hot is too hot for CPU? Sudden reboots?

It depends on the place you are in.

Full cleaning should be done every 6 months (imo)

I agree with Roaster and in fact I would even go as far checking everything out every three months especially if you live ain a dusty particulate environment.

Now I would not rely on just that soaftware for the readings as you can check them in the BIOS with Speccy
Speccy - Free Download - Piriform and in really in depth detail with HW Info - see my ditty
Using HW Info
PART A:
You can test the volts on the PSU with HW Info HWiNFO, HWiNFO32/64 - Download < download the right bit version and close the right hand window select Sensors and scroll down to the power section where you will see what the volts are doing see my pic. In my pic the section (Nuvoton) with VBATT is a dead give away you are in the section for the rail voltages. There are other section titles and one that pops up often is ITE
Now the voltage on the different rails have to be within 5% =+/- of what is required or the machine will not work properly if at all.
IE
12v = 11.4v min to 12.6max
5v = 4.75v min 5.25v max
3.3v = 3.135v min to 3.465v max
See this for the rail voltage info
PSUs 101: A Detailed Look Into Power Supplies (Section 2.)
The original right hand window shows the machine running and is handy for that but for looking at the components in some detail close it and use the main left hand side panel
FOR OTHER COMPONENTS
PART B:
Open each small square with + in it on the section the components are in and then click on the individual component/s (it will highlight in blue) - in the right hand side will appear all sorts of details including brands speeds and other essential info that particular device. See pic for example.

You can use the three opening screens or either use PART A: or B:

Edit use PART B: and then click sensors and the scroll down to the temps of say the CPU see pic

pstein said:

How hot is too hot for an Intel Core i5-2400 CPU?

According to Intel, Tcase max temp for that processor is 72.6 C.

I see two temps in the 90s for "CPUTIN" and "AUXTIN". They apparently relate to the motherboard. I have no idea what acceptable temps are.

HWMonitor CPUID: What is CPUTIN, AUXTIN, SYSTIN and TMPIN3? - Apps - Apps General Discussion

Generally--the temps in the CPU section are 57 and lower, well within the Tcase limit--assuming they are accurate.

Tcase is the temperature measurement using a thermocouple embedded in the center of the heat spreader.

As I understand it, the Tcase limit is maybe where you start to raise your eyebrows, but the processor won't shut down until temps are considerably higher.

I wouldn't be so sure that your shutdown problems are heat-related.

The AUXTIN temperature (94°C) & CPUTIN (93°C) look scary to me.

30 years ago when I worked as a tech, 50°C was the maximum for non-MILSPEC components.

Modern components have a much higher temperature rating, but I still get twitchy if anything in my PC gets over 55°C.

Reading again when did you last renew any thermal compounds??

Well I don't know about the others but could we have some of the other specs of the machine
System Info - See Your System Specs
I ask because that CPU was launched in 2011 which possibly makes the system and it would eb good to know what the mobo is for example and it may not be the CPU that is actually crashing.