Petiolaris complex goes dormant during the dry season (winter in northern Western Australia). Remember the seasons are "reversed" as you cross the equator
From what I can make out the area where Drosera lanata is found looks like the mean day temps during the dry season is in the mid high 80'sF and the mean night temps are in the 50sF.
During the summer (rainy season) the day temps look to be in the mid-high 90sF and night temps in the low 70sF.
The advice I've been given on growing Petiolaris complex by pingman and others is to grow them as tropicals - high humidity warm temps (mid 70's to mid 90's F). I grow mine in a tank and the temps never drop below 72F.
Refer to Pyro's thread How I Grow Petiolaris Complex and pingman's excellent photo essay Petiolaris group in Dormancy