Please help, my sportage is having big transmission problems. The auto gear did not shift to higher mode even when the engine reaches 80km/per hour. Hence engine would become heavier and sound very rough (push to the limits). Please advise. is it due to gear box or engine?

Shift to 4th is conditional to engine temperature going over 140 or something like that. Several in the past have encountered such problem due to faulty temp sensor. Sensor connectors are specially sensitive to corrosion on that car so check for clean connectors and sensor condition.