Keeping cream pies set while browning meringue topping
There could be a few things going on here: 


If it is the meringue that is not holding - you probably need to beat it longer (stiff peaks will hold in bowl if turned upside down for a short time) and add the sugar slowly to ensure that it dissolves before spreading. To test if the sugar is dissolved, pinch a small amount between finger and thumb and rub; if it feels gritty/sandy then the sugar has not dissolved. 
For the filling - most recipes (in my experience) say to spread the meringue over a hot filling, so you don't need to let it cool before adding the meringue. This may vary according to the type of filling you are using though. I'm most familiar with lemon-meringue and chocolate-meringue.
Also for the filling - this depends on the filling. If you are setting the filling using gelatin rather than using the natural coagulating properties of an egg based custard, the gelatin can re-dissolve upon re-heating, but should re-set when cooled. Cornstarch will also re-dissolve when reboiled (though browning your pie should only do this locally at best) and will no longer thicken when cooled.
To brown the meringue use the broil/grill function on the oven and a very high heat setting, not a regular bake. Keeping the door open a bit during the browning should keep the base of the pie cool, so long as you are not putting the pie back into an oven that has recently been used for baking something (i.e. is not radiating lots of heat anyway). 
You can also  brown meringue by using a chef's blowtorch (who doesn't like flames!), these heat locally so you have to wave it around and take care not to scorch the meringue or blast holes in it. There is little chance of heating the rest of the pie with one of these.