Speciation is a function of time. Temperate regions were subjected to frequent glaciations in the past while tropics have remained somewhat undisturbed for millions of years. So tropics had relatively long evolutionary time for species diversification.
Tropics show less seasonal variations , are more constant and predictable as compared to the temperate regions . So they promote niche specialisation and lead to more species diversity.
More solar energy in the tropics another reason for species diversity.