Are we causing a slight rise in local temperatures ?
YES. But it has nothing to do, as you say, with CO2.
The rise in temps is caused by HEAT. Man made HEAT.
Take two jars. Leave one empty, but an electric heater in the other and turn it on. Guess which jar gets hotter.
Every combustion engine and even electric motors generate tremendous amounts of HEAT. Every parking lot and highway is a giant heat sink. Every house, every building that has HEATING and AIR CONDITIONING generates HEAT. We are causing the temperature to rise, but it’s a darn good thing because warmer is better.
Now, can we cause the temperature to RISE so much it goes out of control ? No. Does the planet have the ability to to deal with the man made heat and dissipate it ? Yes.
I doubt that adds up to much. Albedo changes from land use are more prominent of an overall effect. That said, whatever nature is doing is clearly dwarfing either.