That sounds ok and correct, when warming the heater circuit should be warming well before the main flow starts through the rad.
To find the temp gauge sender look around the head or stat cover, my friend had one of these but now sold otherwise I'd have had a look for you.
Like I say maybe more than 1 fault, with engine running unplug the plugs around the stat housing, one will be the temp sender for the ECU, this is not the one you want, but the ecu one should cause the fans to run all the time, ignition on whilst unplugged, so there will no doubt be another seperate sender for the gauge, at least this will identify it for you, I imagine these cooling fans may be ecu controlled, but not sure, I'll find out for you.
In the meantime check all the fuses particularly any with a fan symbol on them.
tabetha