Quote: Go for it, once you brood outside you'll never go back.
If you plan on breeding more in the future, and it sounds like you do, it would be well worth the effort and expenditure to get something set up.
I'd never use a heat lamp in the coop...too scary dangerous.
I only use a heat lamp for the first day or two inside, and only during the day, for observation/assessment of brand new chicks health status.
But if you can get an electrical source safe out to the coop, the heating pad thing is pretty darn safe.
Tho there can be a population limit with a single heating pads, multiples can be set up end to end.
How I did it:
https://www.backyardchickens.com/a/pseudo-brooder-heater-plate
This is a very, very long thread, filled with gratuitous chatter.... but lots of ideas, discussion, successes/fails, and pics:
https://www.backyardchickens.com/t/956958/mama-heating-pad-in-the-brooder-picture-heavy-update
BTW..wanted to mention....Hopefully your mean cock won't pass on his aggression to the female offspring.