Lithium ion battery - measure C rate
To determine the C-rate, you should charge and discharge two cycles very slowly say at 0.1 mA, between say 1.5 V to 4.3 V for your Li-ion (unless it's a very old laptop battery it should be LiCoO2), and measure how long it'll take. The C-rate would be your capacity divided by one hour.

Don't know of a way to measure it using heat or internal resistance.

Batteries generally have an adverse effect when heating up, so unless it is much below freezing, they should be ok.