Hi
I believe you mean INVAR 36? At any rate, as you stated, this is a 36% Ni in Fe alloy. (Very low co-efficient of expansion.) I have not welded this before, but it does not look too difficult. The plain Ar shielding gas will be OK. In addition, H cracking should not be a problem, because the material would be fully austenitic. You can however pick up potential hot cracking problems. I therefore would recommend that you ensure absolute cleanliness when welding this material.
I found this rather handy link:
http://www.hightempmetals.com/techdata/hitempInvar36data.php4
Hope this helps.
Regards
Niekie Jooste
Fabristruct Solutions