Unfortunately it's a common problem, and there doesn't seem to be a fix yet. Some seem to be worse than others, but all of them are apparently set to have the fan running all the time. It probably has to do with the increased power of the sonoma processors, and the fact that IBM decided to use a single fan to cool the cpu, gpu, ram, etc, which leads to the fan being pretty far away from the cpu. So, the processor is warm, which triggers the fan...but, the fan is far away, so it doesn't cool the cpu enough to bring it down to the 'fan off' temp. Thus, you get loud fan and hot computer. Or, perhaps the fan is designed to run all the time, since it cools everything important.
This is mostly speculation, so I don't know if that's really what is happening, but from some people opening up their t43, that's what it looks like (look at the thinkpads.com forums for more info). The 14" thinkpads are more affected than the 15" ones because there is more space inside the case, or the heat-producers are farther from each other, or something to that effect. Also, the 'p's are more affected, for obvious reasons.
People are hoping that a bios update will either allow greater control over the fans, or do Something to help the issue. However, I think that will depend on how Lenovo views it. People have called lenovo and have been told by customer service pple that they don't see anything wrong with the t43's fan. So, if Lenovo decides it's a 'Problem', then they'll probably come out with a 'Fix'. However, if lenovo sees this as the way the sonoma processors are, then they might do nothing.
While the fan always runs on my t43, it's fairly quiet and the computer runs pretty cool. Some people have reported the same thing, while others say their computer is very loud. One person returned his t43 and his replacement was quieter. So, either lenovo has made some change(s), or there is variation and it's luck of the draw. I'm leaning toward luck of the draw, unfortunately, though they might be a tiny bit better now. Only lenovo or someone seeing many t43's could really know.
The best thing you can do now is download centrino hardware control
and undervolt your processor. It lets your computer run a few degrees cooler and also increases battery life. Don't go too low or you'll cause instability and your system will crash, though. Again you should look at the thinkpads forum
for more information than I can tell you. Right now I'm running 800mhz at .716v, vs the standard .998v. My processor runs a few degrees cooler; I'm not sure if there is a fan difference though. It's worth doing either way, imo.