I've got a 1985 Buick LeSabre with the 5.0 litre V8 engine. I just
changed the oil, oil filter, and air filter (1000 miles over I'm
afraid). For the past two days I've been having overheating problems.
The light comes on about half-way through my trip (usually about 15
miles to and from work). This really encouraged me to go get the oil,
etc changed. But it still overheats even after changing the oil.

What could be the cause? From my limited knowledge, I've narrowed it
down to something with the radiator, but I'm not relying on that. I
haven't checked other fluid levels... but that's next on my list.

I would check the thermostat.

First be sure there are no leaking hoses or anything of that nature,
if there , there isnt, then redhoss-ga has it right, you probably need
to change (or just remove) the thermostat.

Presume you have checked water coolant level? I?m not familiar with
your model, but as a basic rule, the temperature warning light (and
temperature gauge) are independent systems which are not actually
linked to any thermostats or temperature control. Often then, it is
the warning system which is faulty and has nothing to do with the
actual temperature.

There are likely to be several temperature control sensors and
thermostats which change the mixture, redirect the coolant and switch
on the fan (if it?s electric). Initially the radiator will be out of
circuit and only comes into operation when the mechanical thermostat
(often near the water pump) opens. If the temperature still rises, the
next line of cooling is the fan. So check that the radiator is warming
up after a few miles. Idling for ten or fifteen minutes will usually
turn on the fan, but under normal out of town driving it?ll never fire
up. Easy enough to check the fan by unplugging it and feeding battery
voltage to it -- but get the polarity right because it might have
suppression diodes incorporated. The mechanical thermostat can be
checked by removing it and placing it in boiling water to see if it
opens but it can be a horror to remove.

A severely lean mixture will cause overheating but the engine won?t
pull properly and make pinking noises so you?d be likely to notice. A
common indicator of overheating is run-on after switch off.

But as I said, the most likely fault is just the sender for the light.
Some can be checked with boiling water and a meter but sometimes the
readings can be misleading, depending upon the interface. Pretty cheap
though, so you could try changing it first. Generally it can be
identified by having someone watching the light and someone else
shorting the single connection to the block.

Best

A car of this age could have many problems:
Worn out water pump
Bad head gasket
Air in the cooling system
clogged water passages
bad thermostat
bad fan clutch
and the list goes on