x2 on the Math Majors. I copied that info above and stored it away in my "Archives of Knowledge".
Here is what I have for the install. All of the parts and materials that I used, I already had laying around the house not being used. So I put those items to good use. So it cost me nothing, but it may cost others who attempt to do this project. I would estimate $60, bulk of the cost being the Bulb (heating element) and 12 Volt Power supply.
1. Start off with a 12Volt (13.6 actual) power supply. I already had one in my storage/male tinkering building for 12Volt Mobile applications. It is important that your power supply have enough amperage to power your "heating element". In my case I need something that could provide 1 Amp of current.
2. Choose a halogen bulb as your heating element. Luckily during the summer the wife had me replace all of the landscape lights with a new design, so I had 8 extra light fixtures laying around. I took one of the fixtures removed the bulb, and plug-in ceramic bulb base to achieve my heating element. The bulb that i had on hand was rated at 10 watts, but it's cone reflector was to large to fit in the rain gauge. So
wearing eye protection I broke the glass reflector off from around it.
3. I drilled a 3/16 inch hole in the bottom of Rain Collector Bucket, to accomadate the power wire. I fed the wire up from the power supply in my building, thru the side vent of the building, along my mast, into my Rain Collector tray, and up into the Rain Collector Bucket base.
4. I then stripped, soldered, and heat shrink wrapped the wires to my ceramic bulb base. At that that point since I was worried about excess heat melting the plastic of the gauge, I looped a wire tie around the wires and unto a surface mount wire-tie base with sticky tape on the other side. The size of the surface mount wire-tie base was perfect to wedge it into some pre-existing slots in the Rain Collector, which should lower the chances of sticky tape from releasing. It is important to keep the assembly from touching any of the internal plastic. One of the benefits of haveing the ceramic base, is the fact that the bulb plugs in to it. So if your bulb goes out, you can replace it easily without resoldering wires. Or if your bulb wattage is to low or high, you can again change the bulb out.
5. I took the "bucket" of the rain collector and lined it with reflective tape (leftover from a heat duct repair) to reflect the bulbs heat around the inside. I then took a Sharpie and colored the inside of the funnel black, to help it absorb some of the heat energy.
6. I reassembled the unit and waited for dusk (my best chance at cold temps not influenced by the sun's radiation). I took a cheap "window thermometer" and taped it to a few various places on the gauge and performed some measurments.
7. With the cheap "window thermometer", I measured the temp on the side of the rain collector bucket to make sure I was not going to melt down. The Top number was current temp outside, Bottom number was the temp measured on the rain collector bucket's side. I let the temp settle for about 20 mins. Hmm, a 25 degree difference that is good.
8. Then I repositioned the "window thermometer" sensor to the top inside the funnel and let it settle for another 20 mins. I took a reading , and
Almost a 50 degree difference, Great!! 
{Sorry about the pic, light was fading}
9. I did not choose to go with a thermostat at this point. The "poor boy" version of one, that I saw at Lowes, a 110volt switching unit came on at 38F and shut off at 50F. It's cost was $12. This large temp swing would cause my heater to be on alot for the 2 months when we get cold here. That would be a waste of energy. Also we are lucky to only get snow about 5 or so times of a year, and only 3 or so of those are usually in a measurable amount. Whenever the forecast calls for winter precip., I will just walk out to the building and turn it on, as I am there already to plug up the battery charger to the Lawn tractor equipped with a small snow blade to clear off our huge driveway.
Additional pics can be see at
http://s266.photobucket.com/albums/ii256/sam2004gp/weather%20station/The glow from afar.....
