On שבת to avoid cooking (בישול) when preparing hot drinks, such as tea or coffee, we pour hot water from the urn (כלי ראשון) into a second vessel (כלי שני), and from the כלי שני to the third vessel (כלי שלישי) where one can prepare the tea without worry of בישול.
According to R' Moshe Feinstein the minimum temperature for cooking (יד סולדת בו) is 110 degrees fahrenheit (but could be as high as 160 degrees https://en.wikipedia.org/wiki/Yad_soledet_bo). Frequently, near the equator, the outside temperature can rise above the temperature of יד סולדת בו.
Assuming that the temperature of יד סולדת בו is 110 degrees, and the outside temperature is above 110 degrees, would one be required to use a כלי שני between pouring from a hot water urn to a cup to prepare a hot drink since everything outside would be at a cooking temperature?
EDIT: Assume (1) the tea leaves are already outside and cooking (roasting) and (2) איו בישול אחר בישול (there is no cooking after cooking) applies to all forms of cooking, not for different types of cooking (i.e. roasting, baking, boiling, etc...)