The initial syllable of this verb tells us that whatever action is being described is happening again. The word’s core derives from the Latin focus, a domestic hearth (the direct source of our word for a centre of interest or activity). The re-warming implied here is not literal but figurative, a revival or refreshment of the spirit or the senses.
The number of writers who have used it may be counted, if not on the fingers of one hand, then certainly on two. The first known was Thomas Coryate of Odcombe in Somerset, an inveterate traveller who died in India aged 40. A decade earlier he traversed much of Europe, frequently on foot, and published an early travel book in 1611, Coryates Crudities, which he announced was “Hastily gobled up in five Moneths travells in France, Savoy, Italy, Rhetia commonly called the Orisons country, Helvetia alias Switzerland, some parts of high Germany and the Netherlands.” He visited Venice in 1608:
It is wholly plaine, and beautified with such abundance of goodly rivers, pleasant meadowes, fruitfull vineyardes, fat pastures, delectable gardens, orchards, woodes, and what not, that the first view thereof did even refocillate my spirits, and tickle my senses with inward joy.
Here’s a rare modern user:
He thought for a moment of the things that magic had accomplished in this very town. ... the innumerable wives who had refocillated a dying passion in their husbands; husbands who had regained the love of their wives ...
Time for a Tiger, by Anthony Burgess, 1956.