Halogen lights intermittent problem

Hi
I have a trio of 20 watt/12 volts halogen lights above my kitchen counter. Every once in a while they just shut off for no apparent reason and then come back on all by themselves within a couple of minutes (or a few seconds).
I believe that they are on the same circuit as the 2 AC oulets that are in the same housing as the light switch. The AC outlets continue to work when the lights have shut themselves off. So it's not a common circuit breaker that's cutting out.
Sometimes flipping the on/off switch a few times seems to bring the lights back on, but they might have come back on on their own without me flipping the switch too. So, I sort of suspect the switch. But I can't make the problem repeat itself by moving the switch in various positions. The switch, for the most part, seems sound.
There are a pair of what look like AC adaptors/transformers that are part of the system. The 1st one is connected directly to the AC. It's hard to tell but the 2nd one is connected to the first one. I figure that the 1st one is a transformer and the 2nd one is an AC/DC adaptor (12 volts DC). They are screwed to the underside of the shelves closest to the switch. Once or twice I've tapped on the 1st one of these and the lights have come back on, but again they might have come back on on their own.
Also, the two of the AC wires (one white and one black) going into the 1st transformer are held together with two of those, I guess you'd call them, thumbscrews. I.e. The wires are held together when you turn the thumbscrew a few times.
Obviously something is shorting out somewhere. But where? I'm hoping that this is not a fire hazard. I really don't want to have to call an electrician. I'm not totally inept but I'm not what you would call a handy man either. I'm new at being a homeowner and have only been in this house for 1 year.
Any tips, suggestions, etc.
--
Joey Goldstein
http://www.joeygoldstein.com
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The power supplies in many of these low-voltage halogen light systems are junk, it appears. Even when they don't give the trouble you've observed, many of them cause horrendous radio interference.
Perce
On 11/27/04 11:33 am Joey Goldstein tossed the following ingredients into the ever-growing pot of cybersoup:

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Before I started replacing components, I'd solder all those connections. You can find an inexpensive soldering kit at Radio Shack. Wire nuts on stranded wire just can't be trusted.
As for hazard, I think your biggest risk would be frustration / blood pressure.
Joey Goldstein wrote:

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im convinced those halogen lights are hazardous period...
randy

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Joey Goldstein wrote:

/snip/
Overtemperature cutout on the 12v transformer(s).
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