Patients receive combined androgen ablation therapy comprising a luteinizing hormone-releasing hormone analogue (i.e., leuprolide acetate intramuscularly once monthly or goserelin subcutaneously every 3 months) and an oral anti-androgen drug (i.e., bicalutamide or nilutamide once daily or flutamide 3 times daily) on days 1-90.* Beginning on day 60 of hormonal therapy, patients receive temsirolimus IV over 30 minutes once weekly. Treatment with temsirolimus continues for up to 36 weeks in the absence of disease progression or unacceptable toxicity.