You don't need language to think.
Language evolved to facilitate communication between individuals. It is neither necessary nor much used for mentation.
Your memory stores information as a complex network of complex concepts. A concept, in this sense, is everything that an individuum found relevant in relation to an object or abstract idea. For example, the concept "table" will, when you first learn it, be stored with your experience of sitting at it and eating something with your family. The concept "table" will therefore encompass both the object table, the sensation of sating hunger, the emotions that being with your family and being cared for evoke, and so on. It won't be an object, but an experience. Later, other meanings (both denotations and connotations) will be added to that initial one, both clarifying and narrowing, and expanding it. In the end, "table" will primarily mean the object itself, as that is the consistent aspect of your experience of that object, and carry with it all the personally significant experiences that for you are related with that object.
At the same time, this concept of "table" will be connected with other concepts, such as family, food, and so on; it will be connected and stored in your memory with representations of the physical sensations that the table causes (what it looks like, how it feels, how your body feels when it sits at a table), and with a linguistic label, that is, the word "table", the purpose of which is to communicate to other persons a very basic and rough idea of the concept in the hope that their concept of this object has some resemblance to or overlapping meaning with your concept of it.
Abstract concepts are the same, the only difference is that there is no physical object at the core of your experiences, but that the verbal label is given to a set of specific experiences (which is the reason why there is so little agreement on what "love" or "freedom" are: we had different experiences labelled the same).
Inside a person, only conscious reasoning is language based, and only in part (other parts are images, sounds, emotions, physiological percepts an so on). Unconscious thought deals with concepts directly: you can imagine unconscious thought as consisting of the multi-sensual input from experiences and the physiological states of being these experiences elicit. At the same time it is unconscious thought that solves problems and makes decisions. It has been shown that conscious thought is merely an after-the-fact representation of unconscious thought (see psychological studies of free will).
therefore, can be (thought to be) done on two levels: the conscious, "linguistic", or the unconscious, "conceptual".
Transferring conscious linguistic thought from one person to another requires that both persons speak the same language.
Transferring unconscious non-linguistic concepts does not require language at all, and you can even transfer your mentation to animals (although they might be understood only to the extent that your experiences match theirs) – which, incidentally, is true for human to human telepathy as well.