It's probably the ISV and/or throttle body needing a good clean.
As for the temperature, firstly check your coolant level and top up if needs be. When the engine is switched off, the coolant is no longer circulating, whilst the engine continues to dissipate its heat into the coolant/oil etc. As the coolant temperature sensor is rather close to the block, I expect it's just the coolant around the sensor heating up further.