I have a 600tt.The temp gets hot very quickly after a 20 min ride, reaching 100 degrees. is this normal

Parts Suppliers. The normal thing to think is "I'll just bypass them", but the tip over sensor cuts power to the engine if you drop the bike riding it.

https://www.google.com/search?q=2001+Triumph+600TT+kickstand+and+tip+over+sensor

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ck for thermostat operation-poss.sticking

My first question is - are both radiator hoses hot too ? I would want to know if the engine is reaching normal temp or not. The engine coolant needs to be over 100 degrees to make heat for the heater.
You could flush the heater core by using pressure to push water from one heater hose to the other. You could have air pockets in the cooling system which would cause both problems you mentioned.

Assuming the radiator is full of coolant, and the engine is reaching normal temp of 190 degrees, you could have a blocked heater core or the temp control valve may not be working on the heater hose.
I would check to see if both heater hoses are getting hot.

Yopu shouldn't have to. Unless your garage gets well over 100 degrees. On a hot summer day the sun beating down on your outdoor condenser, temps can reach over 100 degrees.

Don't run the car without a thermostat. It helps the car to reach operating temps quickly. also helps burn off blow by gasses by keeping the temps up and steady. check your radiator level once driving a few miles. Their may have been some air pockets that purged and need to be replaced with additional fluid.

The unit seems to be working ok....usually the temp probe will reach temp in 5 minutes and it will beep....i sugg for cust to let sit for 15-20 mins for precise cooking.

Normal operating temperature on the bike should not go over 220 degrees F for very long, even in stop & go traffic. Riding down the highway on a hot day you might be 190 F. At start up there won't be a reading until the sensor gets over the minimum which is probably around 100 degrees. You should be able to see it rise after a minute or so of idling. You should hear your fan come on around 190-200 degrees. Your thermostat probably opens at 180, allowing coolant to flow through the radiator and if that does not cool the bike enough the fan comes on next.

When the thermostat calls for heat it should run until the room reaches the temperature setting then shut off. Is the blower motor running and can you feel air coming out of the vents? It sounds like the blower is either not running or putting out enough air to keep the furnace heating. The blower moves the heat from the heat exchanger to the room, if it can't remove enough heat from the heat exchanger there is a limit switch that will shut the burner off if it gets to hot and that's what it sounds like is happening.

That is quite normal - these bikes run very hot and will typically reach temp where fan kicks in (103 deg C) while bike is sitting at idle, even if not particularly hot weather. Needs good airflow through the rad to keep the temp down. 
Fortunately, when fan comes on it lowers the temp quite quickly.