Cognitive testing on people undergoing transgender therapy is rare, but has happened on a few occasions. The Netherlands seem to be the source of much of this research.
Van Goozen et al (1995) found differences in spatial and verbal ability in both female-to-male and male-to-female transsexuals after just three months on hormone therapy.
Hulshoff Pol et al (2006) performed MRIs on transsexuals before and after 4 months on hormones (but before any surgical intervention). This group found structural changes towards normal for the patient's new sex; "The magnitude of this change (i.e. 31 ml over a 4-month period) is striking, since it signifies a decrease in brain volume, which is at least ten times the average decrease of around 2.5 ml per year in healthy adults." In contrast,
Haraldsen et al (2005, Norway) did not find any differences between transsexuals and birth-sex-matched controls on six sex-sensitive areas of cognitive testing, pre-hormones or at 3 and 12 months into hormone therapy.
I generally try to avoid using transsexual studies, because I'm dissatisfied with the controls. I'm not sure of an ethical way to do it, but I'd really like to see studies done with a non-treated transsexual control group. Most theories of transsexuality suggest that there are already differences between transsexual and non-transsexual males and females, and therefore it may not be appropriate to use non-transsexuals as a control group. One interesting confound noted by Haraldsen et al is the socio-economic difference between transsexuals and non-transsexuals in the US; transsexuals tend to have a higher socio-economic class, because it is mostly the people who can afford the rigorous and unsupported medical standards who present for transsexual treatment.