The Aulos tenor sounds good, but the inside of the windway (the slot that you blow into) is shiny plastic. Water vapor from your breath quickly condenses in small droplets on the plastic, which distorts and clogs the airstream, creating the hoarseness and sizzle you describe.
The only sure cure is to warm the top of the head joint up to body temperature, under your arm or stuck in your belt. This happens slowly on the Aulos, which has air spaces inside the head joint -- maybe 10 minutes. If you're playing alone, you might use a hair dryer on the LOW setting.
To clear the condensation temporarily, hold the head joint in your right fist and lay your left index finger across the top of the joint at the bottom of the windway. Blow gently and roll your index finger up until the whistling stops. Then blow hard. (Eventually you'll learn the correct amount of roll-up for your finger.)
If the windway gets too wet for this to work, take off the head joint, hold it in your left fist, block the bottom of the joint on your right palm, AIM THE TOP OF THE WINDWAY AWAY FROM EVERYONE, wrap your lips around the opening at the bottom of the windway and blow hard several times.
The next step is to let the windway dry out for 24 hours. Then gently mix a small squeeze of Dawn liquid dishwashing detergent in a big glass of water. For a plastic head joint, Dip the dry head joint in to the bottom of the windway, balance the joint bottom down on a paper towel and let it dry overnight. For a wood head joint, take a feather or cut a strip of newsprint the width of the windway, dip the tip into the liquid and slide it down to dampen the top and bottom surfaces of the dry windway to make it moist. Again, dry overnight
Even better is an anti-clogging preparation called Duponol. The von Huene Workshop has it as part of their $15 recorder maintenance kit
http://www.vonhuene.com/Default.aspx?tabid=121&txtsearch=maintenance%20kit . Use it the same way as the detergent mix. NEVER SUCK IN THROUGH THE WINDWAY after you use Duponol. It tastes TERRIBLE.
However, I find the Aulos tenor to be heavy and clumsy. I recommend that you sell it and get the Yamaha plastic YRT-304B for $58 at
http://www.lazarsearlymusic.com/recorders_sorted_by_size.htm#Tenor_Recorders . The Yamaha is lighter and easier to handle than the Aulos, it clogs less, and it's a noticeably better recorder.
In fact, when professional recorder players coach workshops, they almost universally use Yamaha plastic recorders -- the YRS-302B ($14.95), the YRA-302B alto ($24.95) and the YRT-304B tenor. (The pros' hand-made recorders are pitched a A-415, a half step lower.) Once, when my wonderful von Huene grenadilla alto was being repaired, I played the Telemann F Major Recorder Concerto with a professional-level reading orchestra, using a Zen-On plastic alto (which is only a little bit less good than the Yamaha), and no one noticed.
Ken Shaw