I've got a simplicial model category $M.$ I'd like to get my hands on the (infinity,1) category of homotopy limit preserving functors from M to Spaces in order to compare it to another simplicial model category. So it would be convenient if I could have a simplicial model category model for the functor category.

I imagine doing something like the following (sketch):

1) find a model category which models the (infinity,1) category: $\textrm{Fun}(N^{hc}_{\bullet}(M^{cf}),\textrm{SSet})$. I'll call such a model category $\textrm{Fun}(M,\textrm{SSet})$

2) use Bousfield localization on the collection of morphisms S = {for each functor F, the comparison maps F(lim d) ---> lim Fd } in $\textrm{Fun}(M,\textrm{SSet})$ to get a model category structure which models the category of homotopy limit preserving functors.

So my questions are

Question 1: Given a simplicial model category $M$, what model category models the functors from $M$ to Spaces?

Question 2: Given a simplicial model category $M$, what model category models the homotopy-limit-preserving functors from $M$ to Spaces?

Answers to my question don't need to address my sketch, but I am curious about whether that will work. References would also be appreciated.