Test current carrying capacity of conductor
You probably need to work out the maximum allowable current density in A/mm² of printed trace cross-section. This will give you a figure you can reuse in further calculations.

If faced with the problem I would try a few approaches:


Print multiple identical test samples.
Use a lab power supply and monitor and record the current as a function of voltage. This will give you a temperature coefficient of resistance which may also be useful.
Test to destruction, recording test conditions such as airflow, ambient temperature, lying on table or hanging in the air, face up / down, etc.




Figure 1. Infrared thermal imaging cameras are used in industrial monitoring of electrical equipment. Source: Fluke.


If possible use an infrared thermal imaging camera to measure the temperature of the element or paper. Be careful to use the correct emissivity factor: shiny metals will have a low value so it may be advantageous to measure the temperature of the back-side of the paper which should have an emissivity value of around 0.95 which is the default for most IR instruments.