I am designing DIY Suana kit from different sources, will the size of the heater changes the performace of sauna like warm up time, any benefit in increasing the heater size, what kind of power supply?

It seems you have a basic knowledge, I would suggest you to request experts advice for setting up the Sauna together. Although sauna was introduced 1500 years ago, the modern sauna is contentiously development ,with tons of cool stuff,.

Just to answer your questions, if your increase the surface area for heater then the temperature is more evenly distributed & heat will be effectively spread out over a larger area to produce a infrared wave. To get therapeutic value you need to generate more heat & spread all over the room with infrared wave & heat.

Generally the sauna temperature is normal to room temperature. When you don't use Sauna for a sometime, then it drops to room . If Sauna is at cold temperature like out door, in area like Northern America or Canada the outside temperature is cold this will take longer to heat up.

When room temperature is close to 70℉ then pre-set sauna room to 140℉ & allow it to warm up for 15 to 20 minutes. It is one of the best practices to warm up with the sauna, once it reaches between 80℉ and 100℉, to gain maximum benefits .

For receiving continues far infrared sauna ray heat sauna room using your sauna & simply set the controller to its highest setting while opening the fresh your session, this way the heaters will continue to emit 100% far infrared heat directed towards your body without shutting down. This way you will get maximum fresh air to ventilate your sauna.

All sauna heaters purchased in North America (USA, Canada etc.,) are recommended to plug directly to wall circuits (110W) with the only breaker on the plug. It is safe to have surge protector at the power source outlet, but always use a certified surge protector.