> hotplate/stirrers listed with a temp range of say 60-300°C
That is the SURFACE TEMPERATURE of the hot plate! Doesn't mean that you can bring a flask to 300°C!
You can easily set any temp you want, even below 60°C, when you use one of these external switching thermometers and an oil or water bath as a heat sink. I've personally put a 300mm (1 foot) diameter glass crystallising dish with 2 liters of oil and a stir bar in it on top of these stirrers, stuck the temp. probe into the oil, and managed to keep the temp at a steady 40°C. Of course the same can be done with much smaller oil baths, I've done the same with only 100ml oil in an 80mm dish too.
The reason is that the built-in sensor in the heating plate of the stirrer is lagging behind the actual heating taking place by a few seconds due to the mass of the hot plate, so one easily overshoots the desired temperature by a few degrees when no heat sink like a water bath or flask is present. The built-in temp probe and electronics aren't that sensitive either, they can tell the difference between 60°C and 70°C but probably not between 60°C and 62°C.
Just use an oil or water bath in conjunction with a switching thermometer and you can achieve exactly the temperature you want in your oil bath. This of course is only useful when you run reactions at a specific temperature, it's completely irrelevant for distillations!!
I'm not fat just horizontally disproportionate.