What is the welding technique heater manufacturers use to connect nichrome wire to copper terminals
The usual method is "spot welding".
The two parts to be joined are pressed into mechanical contact with enough force BUT to make a reasonable but not good connection. A high current pulse from a high energy source is then passed though the connection so that I^R heating causes the two parts to fues.

The normal means of supplying energy is from a large capacitor or capacitor bank. While there is some black magic* in getting it right it is eminently doable at the DIY level. 

Searching Google IMAGES for DIY spot welder  turns up many hits.

Some have used microwave over transformers for this. With a large enough transformer and proper design you may not need a capacitor bank.

I'd say that The poor man's battery tab welder sounds about what you want. 5 X 120,000 Uf 25v CAPS !!!!

And here is a 230VAC to 3 turns out microwave over transformer based (probably) unit. 




Black magic 


This is probably the major means of battery tab attachment and works extremely well indeed in commercial products. You can buy small commercial spot welders and that may be the best approach in more than modest volumes. But doing it yourself should be highly achievable. 

The method works by creating a high temperature but very localised weld on the battery surface but with low enough thermal energy that any internal battery temperature rise is acceptable but while still producing an acceptably reliable weld. 

The magic lies in obtaining proper values for high, very, low enough, acceptable and acceptably. 

"Black magic" is in the practical knowledge gained from experience (yours or others).
I have not done this (I want to) so the following is 'off the cuff' but probably indicative.  

Contact pressure - too low and you don't get enough current.
Too high and resistance is too low and you lose I^2R heating (and the leads get more). 

Some materials will (probably) need more "oomph" than others.
Higher melting point and lower thermal conductivity would be expected to make a difference - but the differences may be other than you expect. eg lower thermal conductivity may help temperatures at a point rise and increase melting - or may not allow a large enough spot size.

Differing materials may take more or less "oomph" than others. 

Preload time prior to energy dump may matter. Or not 

When using an continuous power delivery system operating time will matter.
Too short and tabs break off.
Too long and you may burn through.
Too too long and battery may object.

More ... . 

Much magic can usually be acquired by reading internet accounts from those who have made then AND seem to know what they are talking about. There are very probably user groups who discuss this topic. Candlepower forum members probably do.