To give a taste,
He supervised an operation by which two Romani children were sewn together to create conjoined twins […] Mengele also sought out pregnant women, on whom he would perform vivisections before sending them to the gas chambers.
The cruelty and perversion of these experiments can hardly be overstated. Since similar experimentation on live humans is fundamentally unethical, not much of his “research” can ever be repeated.
Ironically, this means that this situation did present a unique opportunity to perform potentially valuable experiments. For instance, he could unscrupulously perform dissections on intact dead bodies and did a lot of twin studies:
Once Mengele’s assistant rounded up 14 pairs of Roma twins during the night. Mengele placed them on his polished marble dissection table and put them to sleep. He then injected chloroform into their hearts, killing them instantly. Mengele then began dissecting and meticulously noting each piece of the twins' bodies. 
We sometimes hear claims that the results from those experiments have fundamentally influenced our modern understanding of human physiology. For instance, the data from the Nazi experiments on hypothermia are sometimes cited in medical literature [2, 3], although it’s been deemed “unscientific” by others.
A stronger claim is that in fact, all modern text books on physiology incorporate fundamental facts which were gained through these experiments. That is, modern physiology is, at least in some regards, fundamentally dependent on these experiments (since they cannot be repeated). For instance:
Contemporary knowledge concerning the manner in which the human body reacts to freezing is based almost exclusively on these Nazi experiments.  (emphasis mine)
I want to know: is this claim true? Have these experiments any scientific value whatsoever (were they performed rigorously, did they test hypotheses, did they result in new insights?), and are they used in modern medicine. The second, stronger claim might not be falsifiable (too conspiracy-ey?) so feel free to disregard that in your answer, though if somebody does have a definitive answer here, I’d appreciate that.
-  http://www.auschwitz.dk/Mengele.htm
-  MacNeil-Lehrer Report. New York and Washington: PBS, August 1, 1988.
-  Alan C. Burton, Otto G. Edholm. Man in a cold environment: physiological and pathological effects of exposure to low temperatures. London: Edward Arnold, 1955
-  Wikipedia on Nazi human experimentation