I work for Nikwax Waterproofing in the testing lab so I've tested lots of waterproof stuff.
Gore-Tex is nowhere near breathable enough to run in, especially in summer, in fact, nothing with a plastic membrane will breathe enough (Sympatex, Triple Point, PU coatings etc etc). You'd be better off with a showerproof top. Most windproofs these days are showerproof.
If it gets dirty and starts to wet out then you can clean and reproof it (with Nikwax stuff of course - which you can get hold of at any good outdoor store) so it's as good as new. To keep waterproofs breathable the outer has got to be water repellent otherwise you sweat buckets.
The other option is 'Soft Shell', it's a relatively new technology that has started to take off in the outdoor market this year. It's a category of garments that is made up of a number of different fabric types which are (mostly) non-membrane based water repellent clothes for outdoor sports. They sell as 'shower-proof' usually. A good brand is Paramo although they can be rather warm at this time of year. Great for hill walking and mountain sports though. Paramo have sponsored a couple of adventure racing teams and the feedback was excellent.
As noted above in summer rain you're probably better off in something wicking. Make sure you dry off at the end of your run before ou start to get too cold, otherwise you can cramp up.
Cheers
Tweety