Re: halogen spot turns off when it gets hot
This is a safety feature to keep from burning down your house. If you leave the power on they will comeback on after the cool. There are tow types of fixtures, one that must be installed with open air flow and the other that may be cover with insulation. I suspect they are the former and located with either insulation on them or a small closed spaced allowing no air circulation.
Be sure you live your life, because you are a long time dead.-Scottish Proverb