It primarily has to do with the pattern on high and low pressure systems as they present themselves over the continent.
In the southern hemisphere, high pressure systems rotate anticlockwise and low pressure systems rotate clockwise.
Because the north of Australia is close to the equator, generally the north of Australia has a low pressure trough over it. High pressure system tend to centered from the mid latitudes of Australia southwards.
If there is a high pressure system just to the south west of Australia, and particularly if there is a low pressure system just to the south, in the Great Australian Bight, cold air from the south will affect Perth and the south west of Australia.
As the high pressure system moves eastwards a low pressure trough can develop over the west coast of Australia. With or without the trough, the high pressure system moves hot air from the central and northern parts of Australia and Perth and the south west experience hot conditions. If the high pressure system is slow moving this can mean prolonged periods of hot weather - heat wave. A low pressure trough along the west coast reinforces the movement of hot air from the central and northern parts of Australia.
With the same high pressure system over the central region of Australia, as hot is drawn from the central and northern parts of Australia over the western parts of the continent, cooler air from the Southern Ocean is drawn over the eastern part of Australia, particularly the south eastern region where Hobart, Melbourne, Canberra and Sydney are located.
When the high pressure system moves to the east of Australia, particularly to the Tasman Sea, between Australia and New Zealand, hot air from the northern and central parts of Australia will be drawn over the south eastern parts of the country and the regions between Adelaide and Sydney will experience hot conditions.
In the synoptic chart below, for 29 December 2019, there is high pressure systems to the west and east of Australia and low pressure system to the south. The effect of these systems is to draw cold air from the south over Perth and the south west of Australia and hot air from the central and northern parts of Australia to the south east of the country.
This is why one part of the Australia with fry, while the other doesn't.