Whenever i wanted a berry filling for a cake (be it raspberry or strawberry) this is what I did:

I took some of the frosting and put in a bag with just a round tip, put a layer on the inside 'rim' of the cake (this makes a kind of dam so that the filling doesn't squeeze out when you put the next layer on.)

I put fresh fruit AND jam. I took the raspberry jam, put in a bowl and just stir it like mad in order to break up the pectin. This will get it somewhat liquified. I then spread it over the berries to fill the area. put the next layer on and continued.

If it is really warm and you are afraid of the jam getting absorbed into the cake (or it getting somewhat mushy), I would put a very very thin layer (crumb coat thickness) over the cake first and then do the exact same thing. The butter/shortening in the frosting kept the jam and berries where they should be! I also tried to use jam that did NOT have added sugar. I guess I always think of sugar drawing the moisture out of the berries and making them mushy. not sure if that really happens, but that is just what i thought of.)

good luck!
Linda