welcome to coffeesnobs.
All of what you mentioned [temp and cycle wise] sounds about right.
Check out this link from sitesponsor "pidkits", as it plots pretty much what you found [ie max temp 239F=115C, min temp 196=91C]:
A thermostat can be thought of as a bimetalic strip [two straps of different metals with different thermal characteristics taped together]
As it heats each strip will expand at a different rate and eventually will bend causing an electrical contact to open.
Typically in a Silvia this occurs at 110C which is what you are seeing.
The strip requires some cooling before it will return to its original position, hence the 85C. This range is known as a thermal deadband.
Added to the deadband of the thermostat, is the deadband of the system. The heating element of the boiler is quite large with respect to the internal of the boiler and even when the thermostat switches off the power, the thermal energy [heat] stored in the element, will continue to heat the water in the boiler.
Think of an electric stove top, you switch it off and it will still keep heating for a while.
The thermal mass of the brass boiler and the water itself all contribute too.
Optimum temp for a brew is in the range 94 - 96C measured at the puck. Your measurements are taken at the boiler which is approximately 10C higher.
The object is to pull your shot when the brew water is at the right temp.
With your thermometer, you could watch for a boiler temp of say 107C and then pull the shot.
If you dont intend to Keep the thermometer connected, watch the cycle of the machine [take it from a reference such as boiler light goes on]
Google "temp surfing silvia" and youll open a big can of worms
Good luck with it.