Hot tea to iced. Safe?
Please see Food Safety News:  Did You Know Iced Tea Safety which gives the very strict FDA guidelines for iced tea as:


  
  Iced tea sould be brewed at 195 F for 3-5 minutes.
  Iced tea should be stored for no longer than 8 hours.
  The tea brewer, storage dispenser, and faucet should be cleaned daily.
  


while pointing out that "Tea is a beverage with little history of disease transmission."



Applying some common sense, assuming that you:


Keep all of your tea equipment "impeccably clean" as Julia Child used to say
Do not leave it very long at room temperature
Refrigerate it thereafter


given that tea does not have a huge number of nutrients to encourage pathogen growth, the risk should be minimal, although non-zero. 

You must assess your own tolerance for risk, but this is not an activity that is inherently highly dangerous.



Finally, please note that modern refrigerators perform very well, and there is minimal heating of the other foods, even if you put a fairly large volume of tea in the refrigerator to cool.  See:  How effective are modern home refrigerators at keeping other foods cool when hot food is introduced to the space?