Let's model a shirt with a cylinder, and let's flat it in to rectangle. Some 50 cm x 100 cm could be OK for a quick estimate. It's 5000 cm, so 6.25 kW if we want to make it work fast. The OP wrote about 10 minutes. Let's relax it to a little more than 1 kW not to be inconvenient to other home activities and we get a 1 hour time. Probably that will help with heat management too.

But 50x100 is not particularly large (think of bed linen) and yet it could take a lot of space in a house. Maybe some small area handheld device that one can apply to stains and leave it there until it turns off with a timer?