My ASI has an adjustable dial, and at higher altitudes, say over 3000ft, I align my height as a FL, ie1013 mb set, with the OAT on the 'small' window, and read TAS off the now shifted ASI dial.
This can be 20 mph different to previous reading of the IAS.
This leads me to believe temperature should be taken into account in your calc.
Somebody suggested ASIs such as mine are dangerous, I find it simple and invaluable.