no crank, only when cold

'84 KZ700. New battery.
Went to start the bike yesterday, pressed the start button and it just clicked. The solenoid wasn't even firing. I checked connections at all the relevant connectors (except inside the headlight housing). Battery was measured at 11.8V

Do these bikes have a low voltage cutoff for the starter? I bridged the contacts on the starter solenoid, and the bike fired right up. I was not getting voltage at the trigger wires for the solenoid when holding the button. The lights on the rest of the bike dimmed very slightly when i hit the button. The clicking i heard is from something under the right side panel.

I can't currently duplicate the issue, as now that the air temp has hit 70F+, it fires every time I hit the button. I want to find the issue before needing to rely on it starting on a chilly morning. It was maybe 50F when i couldn't get it to crank with the start button.

The lights dimming is normal due to the load on the battery (which at 11.8v is low) if you download the fault finding guide in my signature there is a generic starter circuit “test plan” towards the end 
let me know how you get on, if you are still struggling I will give you some guidance (PS if the lights dimmed without the starter operating we may need to look a little deeper)

How did you measure your battery?
Was the key switch on?
Did you put the probes on the battery posts or the batter terminals?

apologies, i forgot about the electrical gremlin hunting guide. I tried over the weekend to find the issue. Was never able to duplicate the issue in the first place. Though i did give the battery a fresh charge earlier in the week.

F64: probes on battery posts. yes, key was switched to on.

Take off you starter solenoid and put it in the fridge or freezer. Test it on the bench (see if it clicks with 12v across the coil)

Take off your handlebar controll and clean the switch contacts.

Based on what you've said, one of these would most likely tell you what the issue is. Could still potentially be a wire or connector

Found the culprit!
It's the relay between the starter button and the starter solenoid.
I traced the clicking noise to the relay mounted in the rubber boot, under the right side panel.
I gave it a tap while holding the starter button, and everything started working. It then continued to work for the rest of the weekend.
I didnt get a chance to see if it's just dirty connector pins, or if its the relay internal contacts. I'll try to investigate, this week.

Thank you everyone for the input!

EDIT:
Took the cap off. I can see why temperature was an issue. The arms for the relay are pure copper and kind of long. So, the thermal expansion/contraction was shifting the contact alignment to a "burnt" spot when cold. I sanded the face of the contacts with some 1500.
Put the relay in the freezer for an hour, followed by re-testing on bike while still cold, and as it warmed up. Success! I disconnected the heavy wires going to the starter while testing, but the starter solenoid fired each time i tested it.
I wonder if i can find a more reliable (different internal design?) relay that is plug and play.

Starter relay and solenoid? Did they change the design from older bikes? I thought it was just one starter solenoid triggered directly by the starter button.

Do you have a wiring diagram for the 700 (none of the earlier diagrams I have looked at have an additional relay)

It has a "starter control relay" per the diagram. one of these:  www.partzilla.com/product/kawasaki/27002-1051

Carry out the below checks and let me know how you get on

somebody has definitely been messing around.
The bike starts with the clutch out. the kickstand switch has also been removed. heck, it's even got a car horn behind the seat under the plastic!

to be clear, the issue has been resolved. after cleaning the contacts and putting the relay back together, it starts just fine in the cold.

I have some issue with the starter, cracks the engine when cold (slowly), but when engine warm, sometimes no cracking, Today I put a other (revised) starter inside, now problems are solved, good starting cold and hot, also the starting rpm is much higher.
I made a scope grap of the current and voltage during start (with the new starter), see attachment