How does the room gets heated by leaving a fridge open?
Also the radiator emits out the heat in the surrounding. Thus the heat absorbed from the room is released in it and the must neither get cooled nor heated.


You have forgotten a few parts to your system in how a refrigerator pumps heat. You have assumed a spontaneous steady state cycle of:

$$\text{radiator}\underset{\text{conduction}}{\overset{\text{heat pump}}\leftrightharpoons} \text{fridge}$$

But that is not true to move heat from a low-temperature body body to a high-temperature body requires an input of work which is added to the heat dumped into the high-temperature body.



In this case work is done by the compressor which takes in electrical energy and transforms it into work and heat. Since electrical energy is 100% efficient at heating any electrical energy consumed by the compressor is eventually converted into heat either by ohmic heat, efficiency losses or work being converted into heat at the high-temperature body. Since your high-temperature body and low-temperature body are allowed to conduct/convect/radiate/transfer heat between the two sinks, heat overall is added to the room.


  Just before posting this question I have tried to experimentally verify this and observed no change in temperature of the room.


There are a number of problems with this, and why you may not have observed anything.


Rooms are not closed nor isolated systems thus are subject to many thermal variations from light (radiation), drafts (convection), and conduction of heat through walls to/from the outside which can make your results unreliable.
A the heat capacity of a room is very large and it will take a while for your fridge to impart a change that a thermostat/thermometer can detect.
The energy consumed by a refrigerator is relatively small* and it will again take a while for your fridge to impart a change that a thermostat/thermometer can detect.


All and all, such an experiment would require better control than your average room/kitchen. If you did do such a controlled experiment you would observe that the temperature of the room would rise with time due to the heat losses of the compressor.

 *I understand some parents/utility customers (possible yours) may find this statement controversial. Kids do not quote me at home.