Are there any cons to heating orange and grape juice

you know better than I do, it depends on the orange and type of orange. My mom, an executive chef, used to say that you'd allow 1-2 lb of oranges for 1 drinkable cup of orange juice.

I really think, that it's highly dependent on the type of orange. I know naval and blood oranges are the juiciest compared to other varieties.

Sure, you can juice with a blender, as long as (a) the blender is of reasonably good quality and (b) you're not expecting the same kind of yield or quality you'd get with a juicer (electric or manual). You'll also need a very fine strainer, or cheesecloth if you're like me and hate any amount of pulp.

You'll have to peel them first, and try to remove the pips as well (clementines shouldn't have very many, and might even be totally seedless). The pith is less of an issue - some people remove it, some people don't, it's a matter of personal preference. Once the oranges have been "cleaned", start blending them on the lowest speed and gradually bring it up to high. Oranges should have enough juice to blend on their own, but regardless of what fruit you use, be prepared to add water if the blender doesn't seem to be doing much.

Once you've got a fairly consistent purée, pass it through the strainer and mash the pulp against it with the back of a spoon or the bottom of a glass jar. There's your juice. You can throw some pulp (purée) back in if you like that texture.

Fruit purée from a blender doesn't really have the best flavour - it tends to turn out somewhat bitter - so you'll probably want to add a small amount of sugar and/or citric acid to compensate.