Effects of heat: a bit more complicated

Know anyone who does souse vide? Wrap up the battery as waterproof as you can and then put it in the temperature regulated hot water bath for as long as you need.

And I'm not sure how in the world to actually measure the capacity.

The good battery chargers have a testing mode where they discharge the battery and measure the capacity. Normally people use it to check the health of their rechargeable batteries but it works on disposables too. A quick scroll through amazon finds this charger as the least expensive option with a discharge test.

You might be able to modify the charger with extension wires so the battery can be tested a few feet away.