Don't know that frying from cold oil is a good idea; the potato starch used to coat the karaage would very likely absorb too much of the oil and turn out greasy as hell. One of the reasons why frying is done with hot oil is so that the exterior of the breading or batter cooks quickly so that it forms a barrier against the oil to prevent it from absorbing too much of the oil and becoming greasy, heavy or soggy.
If you cut the chicken thigh into bite-sized pieces before marinating with garlic, ginger and soy sauce for about thirty minutes (or overnight) and then dredge it in potato starch right before you fry, you can heat the oil to 350F, fry for 5 minutes, pull out and let drain, then fry again for 5 more minutes for a pretty perfect result.
Source: I used to work in a fast casual Japanese restaurant where chicken karaage was one of the best selling items, and now I southern fry chicken for a living.