Actually, it’s not really a matter of temperate or tropical. A very large number of species that have gone extinct or are highly endangered are island species. Having evolved in the absence of predators and frequently flightless or poor fliers, they have been decimated by introduced cats, rats, weasels, and so on. Also, Hawaiian birds and others have been affected by introduced avian malaria. And of course, since many islands are small, when they are deforested the endemic species have no place else to go.
The avifaunas of Hawaii and New Zealand, as well as many of the Pacific islands, have been decimated. In fact, this process began even before the arrival of Europeans; Polynesian colonization caused an enormous number of extinctions.
Among islands, there may be a greater number of threatened species in the tropics, but this is more a factor of there being a higher diversity of species in the tropics in general than a difference in extinction rates between the tropics and temperate zone.