Heat detectors are now referred to as heat alarms. Smoke alarms consistently respond much faster to typical residential fires than heat alarms. The nationally recognized standard on fire alarms is Standard No. 72, published by the National Fire Protection Association (NFPA). Many fire officials use the chapter on Household Fire Warning Systems to set local requirements for new and existing homes. NFPA 72 does not require heat alarms in either new or existing homes. It does, however, contain recommendations for additional protection in Appendix A, and refers to heat alarms there. The primary recommendations in the appendix are for more smoke alarms, but heat alarms are also addressed.
The reference in the appendix talks about heat alarms for areas in the home where smoke alarms are not recommended. The examples include garages, attics, unheated crawl spaces and kitchens. The air in the spaces like garages can become too hot or cold for smoke alarms to operate properly. Smoke alarms are generally not recommended for kitchens because the cooking may cause nuisance alarms. On the other hand, if the smoke alarm does not cause nuisance alarms, then its location is fine.
For all other spaces like living rooms, dens, dining rooms and bedrooms, the NFPA standard recommends smoke alarms. It cautions you against depending primarily on heat alarms. The Consumer Product Safety Commission takes a similar position.