Will the hot water from the heating tank be filtered water, as well?

I'm just about to make my decision in purchasing the "dual temperature instant hot systems include choice of hot & cold water dispenser, Doulton IP100UC filter, heating tank and complete and comprehensive installation kit ($79.00 value)." But, before I do I have a question, please. I understand that with the filter my cold water will be filtered, but will the hot water from the heating tank be filtered water, as well? If so, wonderful. If not, then how do I get filtered water for my hot water? (I hope that makes sense) :-)

Both water temperatures will be filtered. The installation kit comes with color coded red (hot) and blue (cold) filtered water tubing.

I want to order some your water cooler dispenser for my families, I want the syste that can make the cold and hot, also i want something not above 1200 US Dollars for each.

On the following link you'll find exactly what are you looking for Doulton filtered Instant hot/cold/chilled water systems in five distinctive designs and numerous luxurious finishes.
http://doultonusa.com/Luxury-Plumbing-Fixtures/mt550_instant_hot_water_dispenser.htm