I don't know what the consumer law is like at your location but if an item misbehaves like your unit is doing, I would push very hard for a new unit rather than any sort of repair. In the UK, I can even engage the services of my credit card company if things turn nasty on the refund front.
If you have a digital camera or web cam, use it to record the strange behaviour of your soldering station. A picture or video showing the soldering station and Hakko 191 temp displays would be good. Then show that evidence to the shop owner and request a replacement. I have successfully convinced shops and repair centres of intermittant faults in the past using digital camera evidence.
I have an Audi A4 that created a really strange intermittent whirring noise under the bonnet from new....the Audi local garage checked it and claimed nothing was wrong with the car on three separate occasions. I then recorded the noise using the camcorder function of my digital camera, transferred the audi track to a CD and placed it in the cars Hi-Fi unit. The car was left with the dealer with the instruction to listen to the CD before starting work on the car. Surprise surprise, the mechanics looked a little deeper into the car this time and found that my Air Conditioning pump was faulty from new.....A GBP 1200 part that was just waiting to fail. Fixed under warranty :-)
Its harder to brush off a customer when presented with video or audio evidence of an intermittent fault.