I'm not sure whether I got your question right: you want to calculate the change of a current over temperature via a "current temperature coefficient" ?
In principle such a thing would be possible. But it is not practical as there is no such thing as a "current temperature coefficient". You can do such a calculation if you know all and everything about the whole "current path". Which can be quite exhaustive regarding the temperature dependency of semiconductors, eventual thermo-voltages and so on.
On the other hand: If you did not really get the concept of the temperature coefficient of resistors: this is a property of the material the resistor is made of. These coefficients vary widely between materials and are not constant over temperature (aside from things like PT-100 and other RTDs).
sorry to be negative, but a "current temperature coefficient" does not exist. As written above, a plethora of temperature dependent effects (for single circuit elements) influence the current in a given circuit.