Undenatured whey should be considered a superfood in my opinion. Anything that simultaneously increases glutathione and immunity while lowering insulin resistance and weight is impressive by any standards. One might expect that anything that good for you would also increase testosterone levels. However, this is not the case and, as I will discuss below, it probably lowers baseline testosterone levels in one critical area.
That said, I do not know of any study that has looked at whether or not whey increases or decreases baseline testosterone levels. I have a fear that if a man consumes too much of the standard excitotoxin-loaded wheys, he could potentially damage his hypothalamus - something I document in my page Whey and Free Glutamine - which could lead to a drop in testosterone, since is controlled by the same. However, forgetting about that concern, there is no real evidence that whey has a significant impact on resting testosterone levels. Actually, there is one study on rats that shows that whey delays puberty, but this is just one isolated animal study. 
What there is evidence for is a testosterone-lowering effect post-exercise. As many of you may know, testosterone generally spikes after exercise and so researchers have looked at whey's effect on this phenomenon. One recent study found that whey lowered the cortisol spike that occurs after heavy squatting with weights.  Of course, this should help keep a man from going catabolic - into a muscle-wasting state - because, in general, anything that lowers cortisol will raise testosterone.
However, other research shows that, in some cases at least, whey may actually lower testosterone after a workout (with weights). The first hint of this actually came in 2005 when researchers gave men - again doing heavy resistance training - a mixture of whey and caseinate. They found that both post-exercise growth hormone and testosterone levels were higher in men consuming a placebo than men consuming this protein mixture that included whey.  Of course, one wants those testosterone increases and so this was undoubtedly a bit concerning.
The obvious problem with the above study is that one does not know whether or not the whey or the casein blunted testosterone in this situation. Fortunately, a follow-up study was done in 2008 that looked at whey alone without casein. Again, the post-exercise rise in testosterone was found to be blunted, indicating that whey was the culprit. 
Now, for those of us into building muscle, this may seem to be a real negative for whey. However, the researchers in this study were one step ahead of us and looked at some of the most critical parameters of hypertrophy and stated that:
"In conclusion, the protein ingestion hinders RE-induced increase in serum testosterone in older men but may not significantly affect muscle AR, MGF or IGF-IEa gene expression," where AR = "Androgen Receptor" and MGF / IGF-IEa = "Insulin Like Growth Factor." 
In other words, whey may lose a little out of the gate but seems to more than make up for it down the stretch when it comes to muscle gains. And countless bodybuilders over the decades have used whey successfully for massive gains, so this cannot be too much of an issue, eh?
NOTE: There are now many undenatured wheys out there and I discuss one of them in my page on Undenaturated Whey Protein.
1) International Journal of Toxicology, May 2001, 20(3):165-174, "Developmental Effects and Health Aspects of Soy Protein Isolate, Casein, and Whey in Male and Female Rats"
2) Journal of the American College of Nutrition, 2013, 32(1), "The Effects of Soy and Whey Protein Supplementation on Acute Hormonal Responses to Resistance Exercise in Men"
3) Medicine and Science in Sports and Exercise, 2005, 37(11):1990-1997, "Protein ingestion prior to strength exercise affects blood hormones and metabolism"
4) J Steroid Biochem Mol Biol, 2008 May, 110(1-2):130-7, "Androgen receptors and testosterone in men--effects of protein ingestion, resistance exercise and fiber type"