Brian,
This time of year is generally acknowledged to be too late in the season to be installing Apistan strips in a hive. Apistan is not temperature dependent; doesn't depend on evaporative effects (like formic acid) so there is no reason not to do it - in fact, what other choice do you have if you're trying to save this hive?

Now for the downside for which you should prepare. In order for Apistan to work, the bees have to come into physical contact with the strips. This is the mechanism used for the slow release of the miteacide chemical (fluvalinate) and how the bees disperse it throughout the hive. This is going to be unlikely if they are tightly clustered due to temps. And since the cluster slowly moves around the hive, placing itself over honey stores, they're unlikely to stay in contact with the strips for the proper duration.
It may be worth a try (you'll only be out a few dollars) but in my estimation IF the mite you saw on the adult bee was symptomatic of a larger problem, then your hive is probably no more than a couple of weeks away from collapse and placing Apistan strips is not going to solve the problem.

If it were my hive, I think I'd still try it (assuming you have quick access to Apistan) but I wouldn't be holding my breath for success. The inherent problem is the old biological concept of life cycle growth of populations. When the "prey" (i.e, honeybee) population grows, then the "predator" (mite) population also grows but is lagging behind on the time line. Now the bee population is naturally reducing - like it does at this time of year, every year - the adult mite population is exploding (or has exploded) and the colony is unable to sustain itself and collapses (frequently by absconding).

Hello Brian, can you describe your colony? Is it harvesting pollen? Spotted brood?...Perhaps it is not too late if you have enough population.
Here (Spain) were treating with Bayvarol (flumetrina), with alternance the mite resistence to treatment is not so fast.