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olduser1, do you suspect it could be the something in the engine itself like a gasket or something?
Difficult to say without car service history and or diagnose without hearing/inspecting, but the symptoms you describe may be air lock or cylinder head issue - uncommon on Jazz.
For peace of mind I would ask a mechanic you trust to check if any contaminants in the coolant via the sniffer test its a10 min task.
If the test comes back clear then go for full coolant change + 50/50 mix of good quality antifreeze [ again if your happy
its 2 yr or less] then just add a 50/50 mix of antifreeze to the header tank then drive with heater on full check if heater blows hot. Allow to cool and add more untill max level reached. Burping the air out can be time rich so I would advise so find a local mechanic they are doing jobs all day.
The issue being how long has the coolant been low/leaking and has the engine been driven and overheated.
Another poss cause being a leaking w pump gasket , any how lets know how you set on.
Remeber hot water can give nasty burns