Why does she keep cutting out?

Hi - I am a newbie here but need advice as to why my beloved 1987 GTi cabrio is cutting out.
 It runs beautifully at higher speeds but runs hot in slow-moving traffic, albeit the fan does cut in. After a short while in a traffic jam it will cut out repeatedly, with the temperature visibly rising (but with the fan still cutting in). In addition, when driving at up to but not above about 40 mph it will just occasionally falter and run rough for a while. This does seem like fuel problem but so far no-one has solved the problem.
 
I ran it ticking over at home for what seemed like ages and it was OK but did finally give a little hiccup although it didn't stall. During that time the fan cut in and out to keep the temp under control.
 
It has just recently had a new radiator fitted and new ignition leads.

I am in Haverhill, Suffolk. Anyone any ideas, as my little car is stuck doing nothing without any real prospects of getting better!! I am female and not a teccie so any plain advice would be so welcome, including anyone in the area who might know how to look after Mk 1s! Thank you.

CHECK THE THERMOSTAT IS OPENING FULLY AT THE RIGHT TEMPERATURE.IF SO CHECK THE FUEL/AIR MIXTURE.ALSO THE AIR CONE DISC FOR BEING CENTRED AND FREE MOVING,AND HOPEFULLY THE VW WILL RUN COOL AGAIN.GOOD LUCK.