I agree with you, although the two last suggestions are probably not the right ones. The resistance between battery minus and the ground connection the valve is 0.3 ohms, the resistance between fuel pump relay and positive connection at valve is also 0.3 ohms. Not perfect connection, but not source of a very large "voltage loss" at load either.

I mostly agree with the suggestions that its about bad wirering or bad fuel pump relay or something like that, since the problem seems to "come and go". The cold start valve is working (i can hear it work so to say if i shortcut it (engine off, using the accumulated fuel pressure) or use my newly installed start valve button button I can hear a "click" from the valve and also the sound of gasoline being sprayed (if you understand what I mean). The wire from the computer (control unit is perhapps a better word for it) to the relay is good (?), I have tested it before (if its not a loos connection making it work sometimes and sometimes not).

The resistance between the temp sensor and ground is, if I remember this right, ca 4-5 kohms at 0 C, freezing point, (but Im not very sure about this value, haven't checked this for weeks) and about 180-190 ohms at working temp (87 C) (the latter is a little to low, I know that). Might this small deviation be the cause of all of this???
When I connected a 10 kohm resistance instead of the temp sensor the valve sprayed for several seconds (tied this out to open air, just to test if it was a fine spray or not).

Tried to disconnect the temp sensor, and then the engine was impossible (almost) to start if warm, probably due to flooding of fuel due to open cold start valve, and starts only with gas pedal to the floor... Then I got an idea!... Since the engine also sometimes starts easier with pedal to floor when i try to cold start it another question arises... Is it probable that the computer tells the relay to "over use" the cold start valve (using it to long time) thereby flooding the engine with gasoline (that is, the problem is to much gasoline instead of to little)??? And that THIS is my cold start problem... (I hope not)...

Many thanks to the answers so far, I have got several ideas about what to look for from you...