There a number of ways.
If your materials have sufficient thickness they can be TIG welded.
Thin materials can be furnace brazed.
For low temperature applications there are solders for Aluminum.

How about giving me some numbers, dimensions, and the quantity, is
this a thoudsand or a one off?
Dave


Hi,

I'm wondering what the best way to do this is (I'm not a metal
worker). I have a spherical aluminum mesh, 3" in diameter, sliced in
half. I want to join the circular edge of one of these halves to a
piece of aluminum foil. In addition, the resulting merged unit must
be thermally stable, as it will be exposed to (relatively low) heat
when used (ie., no glues or adhesives). The joining itself will not
be under extreme stress or weight in use, so one or 2 joining spots
are enough, enough to keep it tacked in place.

Is there a welding (or other) process that can accomplish this?

Thank you