Take a look at the radiator itself. It may have been upgraded - you'll see metal sides. Or replaced by the same model- to the best of my knowledge, they don't last that long. In that case it is porbably living on borrowed time - I know that mine gave up at about 60K, but it lived significantly longer for many others.
In any case, radiator replacement is a pretty straightforward DIY job, perfectly documented by now.
Take a look at
http://540i6.com/probsfixes.html for more things to look out for.
My pain points always were window regulators and door locks - check them all for seamless operation.
By the way, clean Carfax doesn't mean jack - came across E28 last year, virgin Carfax record, beaten to hell - none of accidents were ever reported to insurance and were all fixed under a tree. There will be many telltale signs of that, though.
--
http://e39diaries.blogspot.com/ 2003 E39 540i6
http://e28diaries.blogspot.com/ 1988 E28 535i co-pilot