How is the winding temperature of a transformer filled with oil is calculated? since I believe no sensor is directly connected to the winding? Does the the current through a bushing contribute to the temperature value of winding? Any formulas for it?
You don't calculate it, you take an ohm meter and measure it. After it has been running, and the transformer disconnected, you measure the ohms again.
you get the temperature data from the manufacturer or an electrical handbook...
if you have separate temperature sensors you monitor those.
some transformers also have a temperature gauge in the oil level.