Hi, I finally measured the water temp from my Silvia using the method you used, and got a similar reading as you. Approx 82-85 deg C, its a pretty rough way of measuring it if you ask me but hopefully it helps you to know that your machine is heating ok.

I warmed up the machine 30 minutes, then dispensed some water until the light come on, then waited till it came off.

I suggest going straight from the 30 min warm up to the test. The light going off doesn't mean that everything is back up to full temperature.

I can't wait 30 minutes for mine to heat up. I switch it on, let it cycle once on its own, then hit the steam button. Once I'm done with steaming I use the hot water button to refill the boiler for brewing. That refill usually cools the boiler down quickly causing it to reheat again. While it heats I prepare my beans. When the light goes out I flip the brew button quickly to get rid of the flashboil, then in goes the portafilter and out comes the espresso.