As it is described more often that the anticyclonic flow produces the subsidence, clear skies and warm-air advection etc.
Here's some interesting recent work in Australia that discusses this:
The influence of tropical cyclones on heat waves in Southeastern Australia
Teresa J. Parker, Gareth J. Berry, Michael J. Reeder
Geophysical Research Letters 12/2013; 40(23). DOI:10.1002/2013GL058257
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