susanjohnston,
I asked the endocrinologist that I see. He suggests keeping the Tymlos pen in the refrigerator. In the warmest section which I think is the butter keeper.
He says that what disturbs the molecule (degrades the hormone) is the changing of the needle. He advised me to replace the plastic cap that comes on the needle after the injection and to reuse the needle, (which I have been doing with Forteo ). I use the same needle for four days, and keep using the pen until it won't draw anymore.
The pharmacist, the manufacturer and your doctor will probably tell you to discard the pen.
But my guy is really smart.