Short of taking it in and paying the $60-70 to have it professionally cleaned (for which there is no substitute), I have had good results by removing my radiators,lying them on their faces, and filling them with muriatic (pool) acid for about 20-30 minutes.  This does a really good job of getting the gunk and corrosion out of a brass radiator, but do NOT do this on an aluminum one.

I agree with Doug, though, first confirm that the car is actually running hot.

Promised you a picture of my flushing setup. I remove the thermostat and we have a hose hookup on the water heater in the garage, so I can pump hot water. If you wanted to flush through the radiator you would need a second top hose.

Might it be worth it to you to have it boiled out by a radiator shop? I just did some head work and a headgasket on my Mini and as part of it I had the radiator boiled out and had them add a draincock at the bottom (like earlier radiators have) for ease of draining in future. The draincock was a big help when I drained the cooling system to do the head retorque!

Lately Wes I've been recommending that people just solder leads to the chip and mount it using the through-hole on the chip's mounting tab.  In fact, I've been posting links to your web site for your picture/schematic of how to do that.  Where the stabilizer can't be seen (on most LBCs) it sure is an easy (and inexpensive) fix.

And speak of stabilizers. I just got in a new bunch of 7810 regulators from Mouser Electronics. Rock solid 10VDC, and 60-cents each plus a little soldering. Beats the $15 replacements big time. Doug and I have both used the solid state regulators and even put them inside an old stabilizer casing. Clean, and as you say "works a treat"

As a footnote to your question about flushing and concerns about running hot....

Do  NOT assume your temperature gauge is accurate.  Get an infrared thermometer and check the temperature of the thermostat housing and the top tank of the radiator.  It's not at all uncommon for Smiths gauges to be inaccurate.  I have a new radiator in my project Spitfire because the previous owner had disconnected the gauge's voltage stabilizer which made the gauges read way hot.  Check the cheap stuff first.

I made a little adapters out of PVC pipe and fittings that allow me to plumb garden hoses directly into the top and bottom hoses. Works a treat. Will take pics if I can find them (it's been a while).

some of the parts houses sell a two part cleaner, i have used it before and it will clean the cooling system but it can also cause problems if your cooling system, freeze plugs or head gasket are very old it can eat away scale, rust, etc

My method of flushing typically involves me taking off the top rad hoses, rad cap, thermostat, and heater valve hose.  Then I take a garden hose and blast inside the radiator from both openings on top, and I'll blast directly into the head through heater valve and where the top rad hose would connect into it.  Then blast the line going to the heater core.  Depending how you hold your hand over open lines you can get more pressure to different parts of the system.  Eventually the brown stops coming out and you can flush it out with distilled water and go from there.       

so, my car is getting too hot so i decided to flush the system, got it normal temp drained it, green brown color..im guessing rust and coolant. let it cool then refilled with clean distilled water, warmed it up, drained it, slightly cleaner. i did this about 4 times until it ran clear, filled it up again and put in about 1/3 pint super coolant(green version of water wetter). its doing a little better but still getting a little warmer then what i would like. does anybody have anything that works well for them??