Unfortunately, it looks like there is no direct API command for this, but there's a fair chance you may be able to use feSolidExtrude, which can pick surfaces and extrude in both directions to produce the same effect as thickening. This might only be useful if the surface you select is flat.
Otherwise, I suggest you try out:
This can get you the cmdID (Command ID) of a command you want to use. Then, if the command is not specifically documented, you can use:
to run the command once you have determined its id (which I suspect might be 1295, but not 100% sure). Unfortunately, using the feRunCommand method runs the command interactively, and will not allow you to submit the parameters you need for the dialog, you will need to fill them in.
If you don't want to fill these in manually, then I suggest you create a short Program File (not API) which runs the Thicken command. You may need to use some other tricks like Tools | Variables to allocate a Femap variable name to the (loop of ) surface id(s) you have selected, and then use that variable (eg !SrfID) to populate the entity selection box when you run the Thicken command as either a program file or as feRunCommand.
I hope there is something useful amongst all that.