Temperature gauge rises during Traffic jams

I have a 97 Taurus V6 GL. As long as the car is moving I don’t have any problem with temperature stays ¼ level. However when I get stuck on bumper-to-bumper traffic I have noticed that after 5 minutes the engine makes a noise (as if fan is starting or something starts) the temperature then starts rising up all the way to the maximum. The fix for this is to put the car into parking and revving up the engine above 2000 RPM which bring down the temperature to ½ level mark. Please note that the A/C is not on nor is the heating. I can’t figure out what starts in the engine which starts to strain the engine to such an extent that it needs more RPM else the temperature start to rise? Is it the water pump that needs replacement? I have had the Radiator flushed but still the problem persists. Needless to say that it’s causing me a lot of anxiety during traffic jams. Please help!

It might be informative for you to pull over when the "engine makes a noise" to see what it is. Sometimes a radiator flush isn't enough, the flow may be obstructed by deposits to the core. Is hard to check that on a Taurus because of the hidden radiator. Where I live if I use ordinary tap water in the coolant mix, I will have hard water obstructions in the radiator in about 2 years. Only fix for that is a new radiator. A new radiator isn't all that expensive, usually less than $150 and installation isn't difficult if you have patience.

Here are some possible causes that I can think of:
Radiator: may be partially clogged or restricted. Start can and let idle. When temp guage gets to about half way, turn off motor and disconnect battery (to prevent fan from coming on). Feel the radiator for any cold spots. Cold spots are indicative of areas that are clogged or restricted.
Restricted airflow - Make sure there is no debri (bugs, leaves, etc.) on the radiator, Check for damaged or missing fins.
Missing body parts - common to cars that have had front-end collision damage.
Radiator hoses - old hoses can collapse and restrict coolant flow.
Thermostat - may not be opening all the way.
Fan - is the fan coming on when it should? Is the fan causing the correct air-flow? Is the bearing in the fan motor good? Is the fan motor good and turning in the right direction? Is the temp switch controlling the fan working?
Water pump - a bad bearing or worn vanes can restrict coolant flow. Slipping belt.
Radiator cap
Obvious - oil and coolant levels

KimMG - Thanks. I’m inclining towards the theory of the “Fan not causing the correct air-flow”. The noise always sounded like the fan starting but contrary to cooling down the engine it resulted in increasing the temperature. Which makes me think that the fan is causing the problem. During my radiator flush at Jiffy-Lube recently the flow of the coolant was very good from the out hose which I thought was an indication of few radiator clogs. My guess was its either the Water pump or something to do with the Fan. But it never occurred to me that the fan could be propelling opposite air-flow

KimMG - How difficult is it to change the direction of the Fan motor? Would it require chaging the polarity only or does it need an expert?

How do you know the fan is running backwards? Find the temp switch that turns the fan on and off. (bypass the switch) Using a jumper wire or heavy paper clip, connect the two wires together and turn the fan on. It is possible the shaft on the electric motor is broken or the bearings are bad and is causing the fan to bind up and not work.
If the fan is on the bumper side of the radiator, take some strips of paper and hold them against the motor side of the radiator and see if the fan is blowing the strips toward the motor. If the fan is on the motor side of the radiator place the strips on the bumper side of the radiator and see if they are being sucked into the radiator.
Reversing polarity on some electric motors will change the direction they spin.
Is the fan spinning?
Has the car ever been wrecked, engine or transmission replaced, or otherwise taken apart around the radiator? If no, then it is unlikely there are missing parts and this shouldn't be problem. If yes, make sure all mud shields and gaskets are present (some repair shops overlook the need for these parts). Missing parts can affect the direction of the air flow, not allowing the air to circulate properly.
Does turning on the defroster have any effect on engine temp? A heater core is a small radiator. The heater fan is a small radiator fan.

Tech Service Bulletin (TSB) 062000 addresses Fluctuations of the Temperature Gauge.

try changing the water pump I did one for a friend and there was no fins left on the pump it was a 98 wagon