Last week I modified a loom to allow me to weave technical wire ribbons. We use a lot of very fine wire at work, to connect stuff at 300K to stuff at 130mK. Yep, 0.1 degrees above Absolute Zero. We need to use wire that has low thermal conductivity, or we will overwhelm our refrigeration capacity. So we use wire made of manganin alloy, or brass, or some other disordered solid, and use very small diameters.
One way to organize the wire is to line the wires up parallel in a loom, as the warp threads in a weave. The thread adds mechanical stability and strain relief without adding much in the way of thermal conductivity.
I started with the Cricket Rigid Heddle Loom from Schacht Spindle. I removed the rigid heddle plates from the frame bars, and added a pair of aluminum plates to hold the heddle frame together. With one plate off, I put the warp on the loom in a manner very similar to warping an Inkle style loom. I use a pair of double heddles made of thread, so I can make the wire warp continuous, so I don't have to tie each wire length off.
These photos show the test weave, using 26 gauge uninsulated brass wire. The wire we will use for the instruments is 0.005" or 0.003" diameter formvar jacketed twisted pair manganin wire. I used polyester thread for the practice weave. We will use Nomex flame resistant thread for the instrumentation cables.