It wouldn't help for rail already installed, but I wonder if you could insert two corrosion-resistant pins in the rail at some standard distance apart. The pins would be installed when the rail is at its "neutral stress temperature". Then you could use some Go/No Go gauges to quickly check if the rail has expanded or contracted. By measuring the distance you could get a more accurate assessment of the stress state. The accuracy required might be too much, though.

It's an interesting problem. It's simple in theory, but may not have a perfect solution.