Restoring an old fridge; should I add a ground wire

If the new unit does not have a ground connection then it doesn't need one.

The ground wire was for the original thermostat so there should be no bad effects from not having it connected to anything. Any other component in the fridge that requires grounding will still be grounded through it's own wire.

Just make sure that you've insulated the end.

'ben rudgers' is right. There's no analytic solution to your question. A 35 year old fridge is unlikely to operate anywhere near its original design's parameters. You'll have to address this experimentally.

Using a Kill-A-Watt would be ideal. An alternative might be to observe the power consumption of the entire house, with the fridge turned off (turn thermostat off or to the highest temp). Then open the fridge door until you hear the compressor start and observe the power consumption again.

On older whole house power meters, a small metal wheel spun faster when the power consumption went up. If you counted the revolutions per minute with the fridge off, then again with the fridge on, that difference would reflect only the fridge's power consumption. Then you could turn off the fridge and turn on an appliance whose power consumption you know (like a 100 watt lamp or 500 watt hair dryer) to see how fast that makes the meter spin. You could calculate the fridge's wattage based on the ratio of the two spin rates per minute.

I assume that modern house power meters have something similar to that spinning wheel. Or maybe you could log into your power provider's website to check your house's current power consumption and monitor such experimental changes via their virtual meter on the site?