Brand of Computer? Model? Which CPU? How old is Old? How many spindles (two HD's, what size HD, what brand what model #? Is there a problem with optical drive attempting to spin up on a regular basis (with or without media installed)?)
Have any components been upgraded (past year)? Were the upgrades done at retailer? Any changes to Bios?
And what does she do with system . . . Fan staying on even when system is theoretically not doing anything, but system is connected to internet could be a symptom of malware (or symptom of Malware if system was ever connected to internet)
You say pretty clean, in my experience an 'old' laptop, with vents not cleaned on schedule by owner would not be 'pretty' clean and it is possible that a fan can be damaged by compressed air at an average retailer (thus 'pretty' clean and issues with fan could have similar cause)
Yes, a fan can over heat . . . Insulation around electrical connections can break down, voltage regulator and tolerance of motor windings can be at outside limits of QC for each and while it still works can generate more heat then other individual models. Bearings can fail
But in my experience it is unlikely that fan is ultimate source for heat problem if system actually has a heat problem
Two primary heat generators are going to be CPU activity (right mark has a free tool to check that though I think you have to buy a version to get a temp monitor, there are free temp monitors as well) and HD access. Malware can significantly increase both.
So, I'd review power saving settings (is system set to 'sleep' after a given time, Monitor off, HD off, etc. Or is it set to always one?) I'd attempt to accurately monitor CPU activity and HD utilization and do a thorough Malware sweep. At same time it wouldn't hurt to research whether replacing the fan is something you don't want to do or if not start looking for acceptable shop to get quote (in fifteen years I don't think replacing a fan as ever 'fixed' a heat problem, replacing a fan never fixed a 'fan always on' problem)
On the 'more out there' possibilities on 'older', early wide screen consumer laptops there were issues with electrical connections as manfc were switching to 'leadless' solder. There were what could be characterized as 'flex' issues on the motherboard (exacerbated by carrying laptops with one hand). On two different manufacturers I dealt with problems resulting from USB ports having intermittent shorts (USB being designed to supply current to external devices). One of these got to me to recover data after client witnessed flame and smoke shooting out of machine at the 'Computer Doctor' shop to which they had taken it for some reason. My job was actually pretty simple as machine was not fried .. . The USB port was and there were signs that it's MOBO connection had been a 'hotspot' for longer then spectacular flame and smoke moment.
Another weak point (in design) and potential hotspot is AC attachment . . . And you might notice more heat at that point as batteries get older (not just because batts are older but filtered through the various software monitor and control functions of laptop batt, batt recharge software . . . Combined with old batteries)
And it doesn't take all that much dust to impact most laptops cooling functions and ultimate (if not proximal) cause of failure for most electrical devices is insulation break down, the arc of that break down can incrementally increase heat at a number of points, causing fan to work harder and countering it's cooling function at least slightly
And depending on which hemisphere in which you live, if it's summertime you can't ignore ambient temp/humitidy as a factor in laptop heat dissipation. In spring, if I'm going to use AC, in the studio, I'll power up computers and AC at the same time, by this time of year I'll power AC a half hour (though it's actually a function of temp and humidity not time) prior to turning on microprocessors . . . Which is more of a matter of 'holding one's mouth right' then anything of any real value . . . But gut reaction (backed by some non rigorous tests) is that systems run cooler over course of session if I get temp/humidity down first. . . Systems still get hotter, stay hotter and fans run more frequently in summer then winter
In my experience this type of issue is nasty to diagnosis or even be sure whether it is an issue (have a pair of Thinkpad A31p's ( the first of several and now the last pair actually) that are eight years old . . . One has always run hotter, to the touch, hotter monitored internal temps, etc. Then the other . . . From 02 through end of 07 they ran 18-24 hr./day the 'hotter' one always made me nervous . . . Not only was it 'hotter' then it's nearest relative by it seemed hotter then any other laptop I'd owned. Closing in on nine years and it still does it's job. It still think there is a problem that could be diagnosed and perhaps even 'fixed' but after nine years I'm not sure that fixing it could have extended the useful life of that system
In any case good luck.
It's a Packard Bell EasyNote R4622, with Intel Celeron M 360 1.4GHz CPU and 480MB RAM. It's about 4 years old and was a good laptop at the time.
There doesn't seem to be anything wrong with the HD, it stays reasonably cool and runs fine. Nothing wrong with the optical drive either.
The only upgrade has been an upgrade in ram of 256MB, done by myself. This has made the laptop run a hell of a lot better and was really cheap (under £5). The laptop was overheating, with the fan running constantly, before that. My girlfriend says that it has always done it, but it is slightly worse now it's getting older.
No changes to the bios.
She doesn't use it for too much, we know its limits, but the fan is on fully even when it's doing nothing. She mainly uses it for light internet access, writing uni reports, etc.
My girlfriend has told me she took it to PC World around 2 years ago and it would have been cleaned then. Other than that, it hasn't been cleaned. I was surprised to see it so clean inside when I opened it.
The rest of the system, HD and CPU, don't seem to heat up nearly as much as the area round the fan. I was able to monitor HD temp but not CPU with "speedfan" and it ran really cool (35-40C).
I reviewed the power saving settings before posting, doing all the things you recommended, as well as choosing max battery power schemes, etc. She has norton internet security installed which, I think, checks for malware.
I just bought her a new battery because hers was only lasting a few minutes. The ac input and battery seem cool.
We live in Scotland, so ambient temp/humitidy isn't a problem, lol. Today, mid-summer, it was just 60°F.
The cooling pad has made an amazing difference and now it's nowhere near overheating. The only heat underneath is around the fan output, which is still pretty cold compared with no cooling pad. The only problem being that the fan is constantly on, even though it doesn't need to be.
. Under heavy load it was hitting 90. Yet the mobo temperature didn't rise above 30 under load 
. I spent hours cleaning the damn thing and it dropped by 1 degree. And all this was with the side of the case completely removed. Putting a desk fan right up to it dropped it by a mere 2 degrees and made everything so noisy it just wasn't worth it. There was absolutely no logical explanation. I though it might be the case, but I'm still using the same case, with new components and the temperature is back to it's old 38ish.
