Why the tempreture goes up to the almost red mark fast while climbing hill

1997 fiat ulysse 1.9 Turbo Diesel manual. Driving at flat roads the temp. Gauge stays in the middle(normal). Every time the car climbs slope or hill the temp. Quickly goes up almost the red mark and warning(overheating indicator) ask to stop the car light up. Sometimes during traffic jams the temp goes up too but when car has momentum moving speed or coming down slope or hill, the temp gauge decreases to normal. Cooling fan does not switch on automatic when temp. Gauge past half during climbs. The cooling fan sometimes switches on only during idle when not moving. In the morning the cooling fan switches on even when the engine temp gauge is only 1/4 reading (not hot, can still open radiator cap without water spouting out). Why is the fan not switching on when the temp. Is a bit more then half temp gauge. It seems that when the engine is revs high or speeding the temp. Goes past middle and towards hot. Please advice

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