Which of these spices do not lose their tang when heated/boiled?
Paprika and ancho chillies are both from the same family as the hotter peppers and often contain capsaicin, though this depends exactly on which paprika you have. 

Cumin and oregano (and black pepper) are all from other families. I would not rate cumin or oregano as spicy in terms of heat, although cumin can enhance heat when consumed with it. Oregano is the main herb flavour you will find in pasta sauces like bolognese. Cumin is the predominant flavor in many dishes from Mexican/central American and Indian cuisines - if you are making "chili con carne" this is likely a spice you use already. Both of these retain flavour when cooked.

For some non-capsaicin containing alternatives see answers in this thread