There are many versions of Tempura batter so I guess each to his own, as Michael says, the cold water is most important. If you use straight Rice flour you will be making a gluten free batter that is hard to use as it 'sets' almost immediately so I would stick to the AP flour personally then add the Corn starch, baking soda and the baking powder [which I don't think is necessary] the baking powder that is.
Here's part of an article that I have about it that might help but I can't find a link to the complete article I'm afraid. I could email it to you if you so wish.
"Tempura (てんぷら or 天麩羅, tenpura?) refers to classic Japanese deep fried batter-dipped seafood and vegetables. The batter is made of ice cold water and flour. Small dry bite-sized pieces of food are dipped in flour, then in batter, and then deep fried for 2-3 minutes. In high-class restaurants, sesame oil or a mixture of sesame and other cooking oils are used.
Western chefs frequently include tempura dishes on their menus but seldom with 'authentic' results. This largely stems from a misunderstanding about mixing the batter which, in classic cookery must be beaten until homogeneous. Good tempura batter is mixed with chopsticks, but only for a few seconds. This leaves numerous lumps in the mixture and results in the unique tempura structure when cooked. Also crucial is that tempura batter be made freshly, with ice-cold water, in small batches."
I found this in a modified version of the article that I have which I do not totally agree with.
"The batter is often kept cold by adding ice, or by placing the bowl inside a larger bowl with ice in it."
If you were to add ice to an existing batter you would be inviting disaster,
" Over-mixing the batter will result in production of wheat gluten
, which causes the flour mixture to become chewy and dough-like when fried."
I disagree with that statement but would like a chefs opinion on this as I don't believe over mixing will create gluten in any batter. It tends to make it chewy only by removing the air pockets but isn't the gluten already in the product.