How hot can a beverage get without burning the tongue?
Afaik the tongue is not more heat tolerant than other parts of the body, so the minimum temperature to cause burn is about drinking a beverage having 45°C temperature for a long time (more than 5 minutes). The pain threshold of tongue is around 47°C, so you will feel when it really burns.

According to studies the hedonic value of coffee has a maximum by 60°C, and it is significantly lower by safe levels (45°C). Frequent burns of mouth increases the risk of oral cancer. So I think this will be a hard choice... ;-)


  A burn is an injury which is caused by application of heat or chemical
  substances to the external or internal surfaces of the body, which
  causes destruction of tissues. The minimum temperature for producing a
  burn is about 44°C for an exposure of about 5-6 hours or about 65°C
  for two seconds are sufficient to produce burns.



Thermal injuries



  I. With the object of producing standard low-temperature burns in
  animals, and of studying the area of tissue only partly damaged in a
  burn, a burning iron has been made capable of applying temperatures
  from 45°-80°C. to the skin; with this the amount of heat and
  temperature causing skin damage has been studied, and the macroscopic
  and microscopic damage due to graded temperatures have been
  delineated.
  
  
  Graded temperatures of 45°-80°C. have been applied to the skin of shaved, anæsthetised guinea-pigs, and in some cases rats, for times
  varying from 10 sec. to 6 and 10 min. Observations have been made of
  the development of erythema, flare, blanching, blueing, heat fixation,
  incipient blister formation, œdema, and edge wheal, as also upon the
  later scab formation and rate of epithelium regeneration.
  Applications of 47°C. up to 6 minutes produce no visible change.
  At 50°-55°C. applied for 1 minute and over, there is a critical temperature for the development of permanent and irreversible damage;
  in animals good scab formation occurs after burning at this
  temperature.
  After temperatures of 60°-65°C. the epidermis can be peeled off from the exposed area, leaving a punched-out exposed surface area
  somewhat like the exposed human blister.
  



1943 - EXPERIMENTAL THERMAL BURNS, ESPECIALLY THE MODERATE TEMPERATURE BURN
According to Green the pain threshold of tongue is around 46-48°C.  

1985 - Heat pain thresholds in the oral-facial region



  In all experiments, the chosen mean preferred temperature for drinking
  was around 60 °C (140 °F). Black coffee drinkers chose a slightly
  higher mean temperature than drinkers with added creamer, and they
  also chose a slightly lower mean temperature when the flavor was
  stronger. In all cases, consumers tended to choose, on average,
  temperatures for drinking coffee that were above the oral pain
  threshold and the burn damage threshold.



2006 - At What Temperatures Do Consumers Like to Drink Coffee?: Mixing Methods



  Overall, the available results strongly suggest that high-temperature
  beverage drinking increases the risk of EC. Future studies will
  require standardized strategies that allow for combining data, and
  results should be reported by histological subtypes of EC.



High-temperature beverages and Foods and Esophageal Cancer Risk -- A Systematic Review