Update: so I drained transmission fluid, took out about 1.25 litres and now when the car is hot after driving the guage level is slightly below H mark (H is where the Maximum mark is). Looks fine now. I'll check the levels again at night when everything is cold. Also before checking levels I did switch gears to P, R, N, D, D2 and L.
Let's see if this solves the gear shifting problem when cold or else I'll go get the thermostat checked.