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Do you have a scanner that you can check the Engine Coolant Temp (ECT) when cold and before starting the engine? The ECT sensor may be sending the wrong info to the ECM to enrich the fuel injectors when cold. When cold, the ECT temp should be reading about ambient temp. This process works like a choke on a carb engine.
How long have you owned the car and how many miles are on it?
The 87's had a stalling problem from the factory (mine used to stall cold all the time).
I installed a performance PROM (factory Thermostat, minimum HP gain) that eliminated the stall and overall just ran a lot better.