My 04 impala is blowing cold air but is nearly over heating
Are the fans coming on ?
When you turn on your A.C the two fans should automatically come on.
The fans are coming on
Since you say the temp drops when driving sounds like your radiator is partially clogged with dirt and bugs that's why drops when driving its forcing air through the radiator fins so what you need to do is clean out radiator fins with a garden hose and nozzle or better yet a pressure washer this will let you get better air flow across the radiator and A.C condenser coils.
I would also do a Super Radiator Flush.
Looking for a Used Impala in your area?
CarGurus has 25,757 nationwide Impala listings starting at $950.
Search Chevrolet Impala Questions
Chevrolet Impala Experts