Hypothermia (when the body is too cold) is said to occur when the core body temperature of an individual has dropped below 35° celsius. Normal core body temperature is 37°C. (1) Hypothermia is then further subdivided into levels of seriousness (2) (although all can be damaging to health if left for an extended period of time)
- Mild 35–32 °C: shivering, vasoconstriction, liver failure (which would eventually be fatal) or hypo/hyper-glycemia (problems maintaining healthy blood sugar levels, both of which could eventually be fatal).
- Moderate 32–28 °C: pronounced shivering, sufficient vasoconstriction to induce shock, cyanosis in extremities & lips (i.e. they turn blue), muscle mis-coordination becomes more apparent.
- Severe 28–20 °C: this is where your body would start to rapidly give up. Heart rate, respiratory rate and blood pressure fall to dangerous levels (HR of 30bpm would not be uncommon - normally around 70-100). Multiple organs fail and clinical death (where the heart stops beating and breathing ceases) soon occurs.
However, as with most things in human biology, there is a wide scope for variation between individuals. The Swedish media reports the case of a seven year old girl recovering from hypothermia of 13°C (3) (though children are often more resilient than adults).
Hyperthermia (when the body is too hot - known in its acute form as heatstroke) and is medically defined as a core body temperature from 37.5–38.3 °C (4). A body temperature of above 40°C is likely to be fatal due to the damage done to enzymes in critical biochemical pathways (e.g. respiratory enzymes).
As you mentioned burns, I will go into these too. Burns are a result of contact with a hot object or through infra-red (heat) radiation. Contact with hot liquid is referred to as a scald rather than a burn. Tests on animals showed that burns from hot objects start to take effect when the object is at least 50°C and the heat applied for over a minute. (5)
Freeze-burn/frostbite, which is harder to heal than heat burns(6) occurs when vaso-constriction progresses to the degree where blood flow to affected areas is virtually nil. The tissue affected will eventually literally freeze, causing cell destruction. (7) Similarly to hypothermia, frostbite is divided into four degrees (that can be viewed on Wikipedia).
As to the matter of global warming cooking us to death, I would imagine that it would be more indirect changes that got us first. If the average temperature had risen to the necessary 40°C to cause heat-stroke, sea levels would have risen hugely due to the melting of the polar ice caps. Crops and other food sources would likely be affected too, therefore I don't think that global warming is overly likely to directly kill humans.