I suggest
www.acurite.com and get a system with the wireless Internet bridge. The systems usually let you pair more than one sensor too, so you can have outside readings and greenhouse readings all on your phone.
The system you're currently using probably won't be compatible and you'll need to get a whole new one to have it use wifi and see it on your phone. Only other thing I can think of is put an IP camera facing your monitor in the house that you're currently using. That would be a good option if you already have an IP cam.
Another site with good information is
www.wunderground.com they have a list of systems that will do exactly what you're looking more. Most are in the ridiculous price range but there are at least a few affordable options.
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