An engine runs more efficiently when hot. If a thermostat does not shut off properly when cold, it will let cold water pass & it will take longer to warm up. When travelling at speed in winter you may experience the temperature gauge dropping back to cold again. As thermostats age, they tend to open at colder temperatures. Most modern cars have an 82 deg C (180 deg F) thermostat, like the K11.
The OEM nissan thermostat has a rubber seal. This beaks down over time & becomes brittle. Pieces of it will eventually break off, which lets cold water pass. Long before this time, it will also probably open at colder temperatures and/or not seal when cold (i.e. the 3mm gap you saw when cold).
I was checking the operation of my engine using Nissan Data Scan software & noticed that the engine was not operating around 82 degrees when driving, it tended to sit around 76. The temperature did not get into the 90's when idling. After changing the thermostat on my CG10DE, the fan comes on at 97, off at 92.
For those in New Zealand, prices for thermostats as follows:
Partmaster
NZ$18.63 + GST = NZ$20.95 incl GST
REPCO
NZ$17.34 + GST = NZ$19.50 incl GST
Segedin Auto Spares, 379-385 Dominion Rd, Mt Eden.
NZ$12.49 +GST = NZ$14.05 incl GST