sounds like a 'lazy' water-pump, and/or wrong thermostat, though could equally be ignition and or mixture.
Worth changing the water-pump as a precaution to eliminate that one from the list, they are only about £20, and if you are contientiouse, renew all the hoses and clips while you are about it; old ones rot from inside and eventually split, usually when you least need them too. New hoses and pump are a BIG bonus to reliability and save a lot of recoveries.
After that, basic service stuff, which on a series is all very DIYable.
One thing I'd reccomend is a new pair of ignition points and a new condensor; points get worn, and its so much easier to set up a new pair than some old erroded ones, for the sake of a quid or so! While the condensor, again about a quid, is often ignored becouse no-one knows REALLY what the **** it does, and as it has no moving parts or anything, they just leave it alone!
But what they do is soak up current from the ignition circuit when the points open to stop them arcking, and when they break down, the ignition keeps working, just not as well, with the timing getting a bit curiouse as the points arc, and need more frequent adjustment.
Bunging in new poionts and condensor often makes an old engine suddenly 'come alive'.
Then set the points gap and timing, and have a play with the carburettor.
First sort out the cables and linkages for choke and throttle, so that everything is on the stops at both ends of the travel when its supposed to.
Then, clean the air filter out and check the filter hoses.
Then with warm engine, and choke properly off, have a play with the mixture setting.
If needs be, borrow a colour-tune spark plug or portable exhaust analyser to do it with.
An engine running 'weak' will run hot, as will one running too much ignition advance.
At tick-over or on light load, the cooling system is usually more than adequate to cope with the extra heat, but as soon as you rev them up or put them under load, its not, and the needle goes up.
On which topic, may be worth having a look at the temperature sender, and the guage.
Supply voltage should be 10v, curtecy of a balest resistor for the dash panel, but if that's missing guages could be getting 12v rather than ten and guages over reading.
Or you could have a faulty temp sender.
But start with the service stuff, becouse that's useful all ways round and eliminates pottential causes.
Then do the water-pump and hoses, becouse again, big bonus to reliability and worth the doing anyway.
Then if the 'problem' still persists, look at the guages and electrics..... though if funds tight, you might swap the priority of that one with the water pump and hoses.