Is this a EFI engine or carbed?
On EFI, there is a sensor that detects and acts depending on the temp. It fires off the cold start injector. If that sensor is bad, or the cold start injector is clogged(normally with a carbon buildup) you'll have the problem you describe. I'd probably start by pulling the cold start injector and inspecting it. Sometimes you can use some solvent(like a throttle body cleaner) and gentle toothbrushing to clean it.
On a carbed engine, I'm not sure.
On EFI, there is a sensor that detects and acts depending on the temp. It fires off the cold start injector. If that sensor is bad, or the cold start injector is clogged(normally with a carbon buildup) you'll have the problem you describe. I'd probably start by pulling the cold start injector and inspecting it. Sometimes you can use some solvent(like a throttle body cleaner) and gentle toothbrushing to clean it.
On a carbed engine, I'm not sure.