Check the coolant temp senders for the ECU and the cold start injector. Since you say it is related to engine temperature, look at all the things that are temperature sensitive.

Also, just talked to a guy with a somewhat similar problem, in his case the engine would bog down after it warmed up and he drove a little. Tried all sorts of troubleshooting, then they pulled the fuel pump out and found the inlet screen was all plugged with rust.