The actual thermostatic switch mounted on Jazz radiator will turn the fan on and off, it is a simple device, normally a bi-metallic strip that closes the electrical contact when certain temperature reached. If I am reading the wiring diagram properly the same relay used to switch fan - the negative side of the engine fan relay can be grounded either via ECU output ( when aircon selected ) or by the direct acting thermostatic radiator switch ( power to positive side of relay coil is from a fuse that is always live, even with ignition off ). You already know that the engine fan relay is working because it runs the fan when aircon selected, so you are looking at purely the radiator mounted switch and its associated wiring, and the radiator metal work needs an earth return as well. may be a break in wire in the plug or corrosion on spade terminal.
If you know where the engine fan relay is plugged in you can get a muiltimeter and check for voltage on coil pin sockets - ( where the two smaller pins on relay plug in ) one pin will have 12 volts on it, the other pin should read very low resistance ( less than a couple of ohms ) down to car bodywork, if you get an very high or infinity reading down from pin socket to earth then the wiring or switch contact or both are FUBAR..
Has any work been done on radiator or has coolant been replaced recently ? I replaced coolant on a car once and there was a big airlock left in the system, the temperature gauge was hitting the top stop after a few miles, but heater still blowing cold. Another was to check if water pump working is to put heater on hot setting, if it blows cold air then the hot water not circulating...