Here is my take on the differences between Feeling and Thinking:
To use Feeling you have to mentally step into a situation (external or internal). This allows you to fully experience bodily sensations and emotions and to evaluate the situation in a highly personal manner.
For example, you are on the roller coaster and as you go ever more slowly up the track, you can hear the clicking of the wheels and feel yourself weighing backwards into the seat. There is a pause as you look down from a great height. Suddenly you begin to hurtle down the track, and feel your heart beat faster and faster, wind on your face. A scream bursts from your throat as you clench your safety restraint while things go by in blur.
In the same way, you can choose to recall pleasant past memories, as though you were in the experience.
To use Thinking you have to mentally step out of a situation (external or internal). This allows you to dissociate from bodily sensations and emotions so that you can judge the situation impersonally and logically.
For example, you are watching a roller coaster from a distance go slowly up the track and then speed down the other side - some arms are waving about and you can vaguely hear some high-pitched shrieks. You do not experience the emotions you would have if you were on the roller coaster. There will be some emotion - about what is seen.
You can choose to recall unpleasant past memories in the same way, as though you were an observer watching from a distance.
The different ways in which Thinking and Feeling evaluate the same situation lead to the following:
A preference for Thinking will show itself in the use of objective criteria to make decisions. Thinkers will analyze problems in a rational and impersonal way. Judgment is of the cause/effect sequential reasoning type. They will sometimes use external standards, the rules, the procedures. When combined with Intuiting they may use concepts or general principles generated globally and internally.
A preference for Feeling will show itself as making decisions according to what is important to you (Fi - personal values) or others (Fe - collective values).
Feelers' first port of call is to examine how information or circumstances affect individuals. They do not think in cause effect ways, but in web like ways. Diplomacy and tact count for more than some objective "truth" (if there was ever such a thing). It is not about the expression of emotion, although it is probably easier for this preference to do so.