Depending on the size of wrinkle,If Small, I'd use a adhesive syringe and inject some adhesive into the wrinkle and surrounding area. I'd then shield the carpet with something like waxpaper and then use a iron to warm the carpet, As the carpet warms up work the wrinkle out.

If its a large wrinkle, Make a relief cut on top center of the wrinkle the length of the wrinkle. Let one side fall under the other side and overlap. Cut along the overlapped edge triming the pieces even, remove the underlapped piece that you just trimmed free. Your wrinkle should be gone and your piece should be laying flat with just the slit in that you cut. Apply adhesive, adhesive syringes work best so you dont make a mess. Work the "slit" seam back together. Apply pressure for a few minutes and your good to go.

 

You could try some Downy Wrinkle Releaser....... JP