Hello- definitely composting is possible in Qatar. A company called Turba Peat now owned by another company, has been now doing composting on a big scale in Shahineeya (at Al Nakheel), and on the biggest scale in the world in Al Messaied. To get over the high summer temperatures dig into the ground, and shade the compost heap with trees or a pergola, surround with bushes, and keep it moderately damp. Both plastic and metal containers need to be kept in the shade as these will magnify the heat of the sun. Also I think to reduce the heat, decrease the proportion of nitrogen rich fresh materials (the fire of the compost heap) and increase the carbon rich dry materials (the fuel). Add soil organisms that you find in nutrient rich flower or vegetable beds such as worms, earwigs, cockroaches, and woodlice (all spotted here in Doha). The ants are usually present everywhere! If you can't find these, Qatar University nursery has a compost heap with these organisms and it is working very well. The compost heap keeps sinking as it gets broken down by the organisms and new material can be continually added!

As for ready made plastic composters, try Rehab street shops and nurseries (road between the Selwa Road and Haloul Street, not far from Doha British School) or look online.
Happy composting!