Shut off pressure is the pressure developed upstream of the valve if the valve is fully closed during operation. The shut off pressure will depend on what kind of equipment and process you have upstream of the valve.
For centrifugal pump, the shut off pressure is suction pressure + differential head (converted to pressure) at zero flow - see pump curve.
For positive displacement pump, the shut off pressure will be the relieving pressure on the pump discharge PSV - see pump datasheet.
For compressors, similar logic applies except that temperature rises measurably as well. This is not normally the case with liquids.
For a production well, the shut off pressure will be equal to the well shut-in pressure - talk to production operations.
Temperature in liquid service cases should not be significantly different from operating temperature, for gas service it depends on the final discharge pressure and performance of the coolers.
In case of chemical reaction upstram, blocked discharge can lead to a wide variety of scenarios - it all depends on the chemicals and processes involved.
Give us more info = you get better answers, as LittleInch says.
Dejan IVANOVIC
Process Engineer, MSChE