Be aware that a "rate of rise" heat detector provides no protection against a slow smoldering fire, the type that kills due to smoke inhalation. Also, by the time that the interior of the space reaches the setpoint of the rate of rise detector, chances are that it will be very difficult to extinguish the fire as it will have become well established.
You are correct that you may generate false alarms with welding equipment and photoelectric smoke detectors, and certainly would have problems with the ionization type of detectors which have a history of false alarms in this type of application. However, you are placing yourself at a disadvantage by not using a smoke detector.
Careful selection and installation of the correct type of smoke detector will provide you advance warning of combustion byproducts as compared to the heat detector alone. I suggest that you consult with NFPA or a local fire safety expert for a recommendation.
Also, proper venting of the welding gases/smoke will go a long way to preventing false alarms, as well as assuring your safety and comfort during welding operations.
As always, offered only a opinion