Not sure if you have seen this yet but these are some outstanding culture notes and tips from Mr. Harry at H&R Nurseries
C walkeriana - Tips for Growing & Blooming
I’ve followed these to a T, taking into consideration my conditions, and I have had fantastic results. And that is without having any experience with Cattleyas prior to starting to grow walkerianas... A rootless purchase from last year is recovering well, seedlings are doing great, and I have several in spike or bud. Two of mine currently in bud have experienced nights in the low 50s but warm up during the day. They all get watered early on warm sunny days and are potted in a way that they dry off in a few hours. I try to increase the light in winter when they are not in bud and grow them a bit shadier (bright but filtered) in the summer
Keeping it as warm as possible for now while you have it in the sphagnum tent would probably be beneficial. Cold and damp can be a major issue for these. But, as others have said, you may not see much happening till early spring when this hits a growth cycle. But when they grow, they can really grow.
This was also one of the project plants a few year ago. It might be helpful to read through that thread, under the member projects section, as well. It’s a long one but worth sifting through