I hate to disagree with you, but for a P4, 57C is really pretty good and
possibly below the average under stress. The P4s usually won't start any
thermal throttling until well over 70C. I can get my Core 2 Duo pretty close
to 50C with Orthos or other CPU stressing utilities and it is liquid cooled,
so a P4 at 57C is not bad at all. If I were the OP, I would try running with
just one stick of memory at a time and see if one of them is causing his
problems. I have seen memory pass memtest and still have issues within the
OS.

Ed

Run Stress Prime with each stick by itself. Compare test results
between the two test runs. If one case fails and the other one doesn't,
that could be confirming what your other tests are showing (that failure
follows the memory stick).

If the "good stick" of RAM can run Stress Prime for as long as you're
willing to wait, then I guess that tells you that 58C is not too much.

As for whether you should tolerate a 58C CPU temperature, you are
using a 3.8GHz P4, so it is bound to get hot. There are some nice
heatpipe coolers you can use, to reduce the temp -- how much money
do you want to spend to fix it ?

For a cooler, the Typhoon places an emphasis on quiet, and the fan
should probably run a bit faster than it does. It uses a 120mm square
fan.

http://www.newegg.com/Product/ProductReview.aspx?Item=N82E16835106061

And volume-wise, this is probably the biggest one you can buy. Some
people have trouble fitting this inside their computer case. Tuniq
Tower is the same price as the Typhoon.

http://www.newegg.com/Product/ProductReview.aspx?Item=N82E16835154001

There are plenty of other candidates on the pages of Newegg - read
the reviews to see what kind of performance the customers got. Many
people will be using lower power processors than a 3.8GHz P4, so you
have to find reviews where people used a hot processor. For example,
an AMD 6000+ X2 is 125W under load, and would be a good test for any
heatsink. A puny Core2 Duo at 65W, is hardly a good test of a cooler,
and a lot of people use those.

The 3.8GHz P4 here, is 115W TDP.
http://processorfinder.intel.com/details.aspx?sSpec=SL84Y

For an Intel processor, there are a couple critical temperatures.
There is the throttle temperature, where internally the processor
slows down, to try to cool itself off. On some processors, this
temp is in the 65C to 70C range. The second temperature point,
is THERMTRIP, which causes the computer to shut off. This temp
varies by product family. On some older processors, it was set
way high (135C). More recent processors, THERMTRIP at 20C more than
the throttle temp.

So 58C is still OK, with respect to those two trip points. The
first trip point robs you of performance, while the second
trip point shuts the computer off. And at 58C, you've avoided
both of those conditions.

The math behind coolers is pretty simple. You have the room temp
(like 25C). Increasing the room temp, results in the computer
temps rising to the same degree. A well cooled computer case might
run around 32C (i.e. 7C more than R.T.). The CPU temp would be

   CPU_temp = Case_air_temp + (Processor_Power * Thermal_Resistance)

Say you had a Zalman 9500A cooler for your CPU. The product page
lists thermal resistance as 0.12C/W at max fan speed, and 0.16C/W
with the fan speed adjusted for quiet.

http://www.zalman.co.kr/eng/product/view.asp?idx=247&code=009

   CPU_Temp = 32C + (115W * 0.12C/W) = 45.8C at max fan speed,
                                       and running Stress Prime

If your case isn't cooled very well, then it'll run above the 32C
figure. If the heatsink you buy, has a thermal resistance higher than
0.12C/W, then the resulting CPU temperature will be warmer.

Not all heatsinks have a measured thermal resistance (theta_R) value,
and you may have to go looking for good review articles, to get a
measured value. Note that not all review sites are equally gifted
when it comes to heatsink reviews, and some sites only do the reviews
to get themselves a free cooler.

   Paul

I don't have the spec numbers for your processor.  However you take
that number. That is the temperature it can be at when the room is at
100 degrees F.  So subtract 20 degrees C from that number.  That is
the temperature the CPU must be at in a 70 degree room.  What is the
max temperature of your CPU?  70 degrees?  Then CPU must not fail at
58 degrees.  IOW that is a hardware failure.

 Selecting heatsink assemblies starts by doing calculations.  You
should know from CPU specs its average power consumption (in watts).
Heatsink manufacturer (if he is honest) must provide the 'degree C per
watt' number.  Now you know the temperature difference between
exterior air and CPU.  Does the heatsink perform according to its
'degree C per watt' calculations?  Is the heatsink really sufficient?

 We solve problems by doing the numbers (the hypothesis) and then
confirming those numbers with the experiment.  Some reasons for higher
heat are bad heatsink surfaces (which is why thermal compound is
necessary) or excessive thermal compound.  Too much is bad.  Too
little causes no problem are a properly machined heatsink.

 The only time dust is a problem is when dust completely obstructs
airflow.  Heatsink designs must include dust coatings.  And if dust is
so massive as to close the heatsink, then computer chassis is moving
too much air or computer is being used in an industrial environment -
heavy dust settles daily on everything.

 I do not see where you performed comprehensive hardware diagnostics
using heat (the hairdryer).   Effective diagnostics execute without
Windows even loaded.  If your computer manufacturer is not
responsible, then you must obtain third party diagnostics or
diagnostics from each component manufacturer.  One popular memory
diagnostic is Memtst86.  Each diagnostic is executed at room temperate
AND at elevated temperatures.

 I also do not see where voltages are confirmed - that two minute
procedure defined above at  http://tinyurl.com/yvf9vh .  Expect
temperature related failures to occur if voltage integrity is not
confirmed.  It was not a suggestion.  It was a very strongest
recommendation.  Your symptoms such as running for two month OK are
typical of a computer that has always had voltage problems.