Rodney, let's backtrack a bit.
Have you covered the basics? Is the cooling system full? Early LSs were known for leaking overflow bottles and/or thermostat housings. As the coolant level dropped, airlocks were created within the system.
Please be clear about what you mean by "overheating".
Does the gauge go into the red?
Does the little red thermometer come on?
Does your message centre display "check engine temp", or "engine power reduced", then possibly "pull off road safely"?
When the A/C is on, the fan runs constantly. When it's not, the fan is turned on by the PCM only when coolant temperature gets high enough to demand it.
At idle or in stop and go traffic, it is absolutely NORMAL for the temperature gauge needle to rise above the horizontal position, sometimes almost 2/3 of the way up, before the fan comes on and drops it back down.
Is that all you've got?