Question

how to detect transformer oil tempureture

Answer 1

Apart from the obvious methods which can easily be found by Googling here is a description of an interesting method.
http://www.fasint.it/pdf_formazione/Monitoring_HV_Power_T_using_Fibreoptics.pdf

Answer 2

thanks

Answer 3

what is the relationship between temperature and resistance?

Answer 4

For what material as the relationship can be almost anything?
Also the temperature is also important.
For a metal over a small temperature range the increase in resistance is proportional to the increase in temperature.
One way of writing this is

R(t) = R(0) x (1 + a t)

where R(t) is the resistance at a temperature t degrees Celsius and R(0) is the resistance at 0 degrees Celsius. a is a constant called the temperature coefficient of resistance and its value depends on the metal.