if your 250w is doing fine then i wouldn't spend anything for an upgrade. at the same time, remember that you might see the 250w not putting out enough power sometime in the future (random power shut downs). SIW won't give you the power supply temperature, but should give you alll the others, like hard drive, cabinet temp,, cpu temp etc. there might be other apps that will give you power supply monitoring, i have read about them but can't remember them off-hand. SIW will give you voltage readings on your PSU, but not amperage readings or temperatures.
Yes the VGA connection is slowly dying out , also remember, chances are that you may also have an onboard VGA output. it is a standard VGA jack that you should see on the back of your cabinet. it isn't as sweet as a dedicated gfx card, but will get you by in a pinch. The other jack on your 6450 besides the VGA and the HDMI is a DVI. you can tell if it is convertible to a VGA if it has four pins around the wide pin. that is a DVI-I and you can get a cheap passive adapter to convert it to a VGA output.
if you can get SIW and if it works on your machine to read temperatures , the typical shut down heat range is around 90 celsius for CPU and around 106 celsius (220 F) for gfx card. Most users start seeing a danger zone around 65-75 celsius anywhere.I have seen instances where SIW wasn't compatible and wouldn't provide the info, but i can testify that it works on my xp32 machine. if it isn't giving you the desired result, you can try for HWmonitor to check your temps, it is free also. i haven't seen an instance where HW monitor didn't work. then there is another app called speccy, which i don't recommend because it has been known to clog data pipelines before. it may work for you, but i know it has hung up my PC a few times. I would use those apps to monitor your temperatures as you are playing games to see just how the malfunctioned case fan is letting the heat accumulate.
that is one more good thing about 6450 also, low heat generation. some of those super-charged gfx cards will hover in the 80c range during normal use.
I don't know for certain how the heat will accumulate if you are gaming on your PC without the case fan blowing the heat out of the cabinet. you may be able to get by with using a household fan to get the heat out of there, just try to get it as close to the cabinet as possible. I know this one guy who has been jamming with black ops 2 for days at a time without a case fan, that blew my mind. He was none the wiser. his cpu fan and his gpu fan was doing fine by themselves somehow.
yes, the 92mm 3 pin case fan should be installed at the first oppurtunity! keep in mind that those fans accumulate dust and it keeps them from spinning the way they should, so periodic cleaning is a good approach. (2x a year maybe)