There is(are) a lot of temptation(s) out there in the world

Temptation as a concept is uncountable. You may consider that the most appropriate for your sentence.

Temptations (individual things that tempt us) are countable. I succumbed to the temptation to have another glass of wine.

There is/are [a lot of temptation(s)] out there in the world.*

"Lot" is one of a few non-count quantificational nouns that are said to be number-transparent in that the number of the whole noun phrase is determined not by the head noun "lot" but by the noun that is complement to the preposition "of".

In the case of the non-count abstract noun "temptation" the noun phrase is deemed to be singular so the verb should also be singular, i.e. "is".

By contrast, "temptations" is a plural count noun and thus the noun phrase is plural, requiring the plural verb "are".