MEANING:
Noun: A warmer. (Anything to warm somebody up, including pieces of cloth or alcoholic drinks.)
Lämmike appears in our example in the partitive singular, lämmikettä
DERIVED FROM:
Lämmike comes from lämmin (”warm”) + -ke (a suffix sometimes used to produce nouns from adjectives.)
EXTRA CREDIT:
The other word in the phrase, piristystä, means ”a cheering up,” or perhaps a better translation here is ”jazz up!”
The basic meaning is that this coffee will warm you up and perk you up. A better colloquial translation of the slogan ”lämmikettä, piristystä!” is very welcome.