If the Scale Bar is made of the same material as the object being measured, applying the scale distance(s) should scale the entire object to the temperature at which the Scale Bar was calibrated. If you want to scale the measurement to another temperature (for example, the ambient temperature at the time of measurement), you can apply the temperature coefficient of the Scale Bar material to the calibrated Scale Bar distance.
If the Scale Bar material is made of a different material than the measured material, then you must apply the temperature coefficient of the Scale Bar material to the calibrated Scale Bar distance to get the true distance at the ambient temperature. Then, you can scale the measured material to any temperature by applying the temperature coefficient of the measured material to the object measurement. However, in both cases, we have assumed the measured object and the Scale Bar are both at the same temperature. If the two have significantly different thermal masses, and the temperature has changed significantly, this assumption will not hold. Fortunately most measurements are completed so quickly that there will be very little scale change due to temperature.