1999 Honda Civic heats in traffic with air on

This car has a new radiator, cap, hose, water pump, timing belt, fan relay, air compressor clutch relay, tempurature sending unit, temperature sensor and air removed. The fan does come on but probably not quick enough and does not stay on very long (sometimes). It does not lose water nor have signs of a head gasket problem. It has not overheated while I have owned it. The problem has developed this summer.

If you turn the air as cold as possible and the fan up the tempurature will climb in stop and go traffic. The tempurature will drop as speed is increased.

The temperature will stay low if the air is moderately cold and the fan is low.

The fan does come on but at various levels of tempurature.

With the air on should the engine fan be on constantly or is it controlled by the tempurature? It has a separate condensor radiator (and fan) for the air conditioning and a separate radiator with it's own fan for the engine. The condensor fan runs continuously with the air on. The engine fan comes on based on temperature.

It acts like the engine fan is not coming on when it should or staying on long enough.