I recently posted a thread about this.
I had similar symptoms and found a bad connection on the sensor.
If your 300e's sensor is the same as my E200, and I think it is,
then it should be 325 Ohms @ 80degrees C
1200 Ohms @ 40C, and
Mine went totally open circuit, infinity Ohms, led the ECU to think the coolant water was minus God-knows-what, and went to full rich. As soon as the lambda probe caught up, its sorted things out.
So it started fine from cold, but hot starting was really difficult.
Hope this helps
E200 1994 108k miles