Here's a technical answer.
1. Assuming you could get starting fluid (or some portion of it) into the tube and sealed, it's coefficient of thermal expansion is quite different from ether, hence the temperature it reads will not be correct.
2. Starting fluid is a liquid only when kept under pressure or VERY cold. Freezer temperatures will not keep it liquid. In the freezer some components will stay liquid, some will evaporate.
3. Teflon wrapped machine thread will not likely seal in this application.
4. You are playing with a potential bomb doing this.