Is it possible to think in a second language?
It is possible for some people to think in a second language. And given that you are asking about possibility, to some extent anecdotes are evidence.


Many children who change linguistic communities at a young age lose the ability to talk in their first language. This is particularly the case where the first language is different to the language in which parents speak to their children. 
In less extreme cases I have friends who came to an English speaking country at a young age, but still retained the ability to speak in their native language. Nonetheless, the vast majority of the time, they speak English. I assume that at a certain point, they switched from primarily thinking in their native language to primarily thinking in English. One friend mentioned the experience of when at around age 14, his dreams began to switch from being in Polish to being in English.


I guess the interesting question is whether there are limits to this, such as when the second language is not learnt until teenage years or adulthood.

In terms of a few hypotheses, I would think that ability to think in a second language would be linked to (a) greater fluency with the second language which in turn would be linked to experience and training and (b) specific primary training in the content of the thoughts in the second language (e.g., if you study a subject at university in the second language and thus you may know the terms better in the second language). Also from my limited experience of learning French, it felt like there was a degree of choice whereby I could actively try to think in French. That said, the cognitive associations between underlying concept, English word, and French word were pretty strong. Thus, the subjective experience of thinking in French and translating from English to French was often subtle.

Note also that I'd still be interested in any research that has specifically studied this phenomena.