‘Thinking’ refers to a process of thought, forming an opinion or judgment. When expressing ‘I am thinking of’ you are letting someone know what you are personally thinking.
Here are some examples:
“I’m thinking of checking out the new movie.”
“I’m thinking of filming my vacation.”
“I’m thinking of following a healthy diet.”
“I’m thinking of handing out flyers describing our business.”
“I’m thinking of increasing my work load.”
“I am thinking of introducing myself to him.”
“I am thinking of launching a new website.”
“I am thinking of moving to a new city.”
“I am thinking of offering her the position.”
“I am thinking of opening up a store.“