They have always been exhaust heat activated warm-up thermostats.
The additional 1969 solenoid on the MFI pump is an additional 'cold start enrichment' device that forces the main rack full rich during cranking, limited by a 2nd Thermo-Time Switch.

I agree with 356RS, perhaps a cleaning of the thermostat is in order.
This is normal, useful mainteinance.

Measuring the fuel pressure and exhaust mixture during these events will help with the diagnosis.

Best,
Grady

I have the same problem on my 69 E. In my case, it is the thermostat on the pump. I built a rig that replaced the thermostat with a plate and screw and demonstrated that I could start and immediately lean it out with the screw.
Two other things helped a little. I trimmed up the heater hose to make sure I had a good seal. I looked at the thermostat and saw that two of the disks were reversed. A Porsche mechanic said there was a bulletin to do this to slow down the extension of the bellows. At any rate, I turned them around again. So far Im living with it. I drive off quickly, with the idle lever up a bit, just to get the heat flowing to the bellows.

I can almost say is solved.

The thermostat was clean and in good shape (I had already checked months ago). Thanks to your help I was almost sure the problem was there so to check, I tried disconnecting pipe from heat exchanger and heat it using a hair dryer while my son started the car.
The result... the car started perfectly!!! so the problem was in the heat coming from heat exchangers.
I did a CLOSE look at all the pipes and I discovered a crack in the pipe from fan to heat exchanger (the big one, 60mm) that was hidden!!!
SO EASY!!! just a $20 heater hose!!!

I tried provisionally (I didn't have a spare one) and it worked perfectly!!!

One more reason to discover a couple of conclusions:
1. Always keep cool and think logically.
2. Things that seem easy and not important ARE also important (a simple hose...)

THANKS ALL!!!