My Mini Pajero does exactly same in the cold mornings. In "D" it is actually in 3rd gear till engine is fully warmed up (or ATF reaches its operating temperature). In summers it is perfectly OK.
Mitsubishi calls it "Safe Mode".
Tomorrow, I am going to change the ATF from KIXX to Mitsubishi SP-III (quite expensive) and see the results. Some people say that warming up the TCU with hot air solves the issue, I have yet to check it. Although I bought heating plates to mount under the TCU but never could find time to mount those and see the results.
Radiator fan in Mini is clutch type and directly mounted on the engine pulley. It does work well if fluid clutch is working properly. But in hilly areas, I have faced some issues with this type of fan. So I am thinking to change my fan to electric type.