Ohmy, Don’t use Goop if you want to save the wood finish. I halogen heaters love Goop but not for this project.
Get yourself a can of WD-40 which you will find with spray oils DIY most likely in the automotive section. It is not really an oil and it has a thousand uses, one of which is removing sticky residue without harming the finish. You gardening will have to rub quite a halogen heaters bit but in the end there will be no damage and it works like a charm.
Go to this WD-40 home site and look up the 2000 uses for it.