I recently got a 1985 K-100....and just joined this great forum... I love the bike. On good days, it purrs and performs like a thoroughbred. Great. On bad days, it back fires and lags off the stop light and generally seems wonky in the way the engine responds to throttle (too much fuel choking? Too little? ) also get the overheat temp light... But the coolant level fine. Weird. And finally, sometimes I get white smoke come out exhaust when I start it up. Again, sometimes not. Haven't serviced it yet-no time- . Maybe plugs change, oil and cool flush. Check cool fan. These are my lovely dilemmas. Cheers all!
Omegaman

Most important to check the cooling fan. They do go wrong, seize or won't turn at all. If the temp light comes on check if fan comes on. I don't know which comes on first but I think it should be the fan. If it is not coming on you can check by running a separate live supply and see if it comes on. If it doesn't work then its probably kaput. The fan is a known weakness.

Agree with Olaf on checking the fan. The fan should kick in before the light comes on. Let it tickover on the centrestand and the fan should come on after 10-15 minutes.
It's not unheard of for them to seize up. Thirty year old electrical connections can cause problems, too.
Regarding the smoke. Are you sure its white?
Common issue with early K's is that if you switch off too quickly after you pull up, you can get oil being burnt through the exhaust. Especially if you put it on the sidestand immediately.
Easily cured!
When you stop,let the engine tickover for 8-10 seconds before you switch off. You can then park it on either stand and no more smoke when you start again. 
Later K's, '86 onwards, had piston ring mods that prevented this from happening. Wouldn't worry about it though.

Thanks guys! Will give it a go and let you know.
Cheers and great riding.

The smoke issue is a well known one and caused by the oil getting past the rings when parked on the side stand.  The cylinders face slightly down and oil draining from above collects in the bores and gets past the rings into the combustion chamber and exhaust. john said the post 87 bikes had a correction mod but my 93 K1100 still does it.
The fan should come on at 103°C and the light at 111°C so check the fan as suggested.
Just getting hot should not cause bad running in itself, check the electrical connections under the tank and treat with a contact cleaner like Deoxit. The hall sensors that control base ignition timing are prone to failure with heat but usually it is a very definite go/no go situation with them but would pay to check by heating with a hair dryer when the engine is cold and seeing if it has an effect.