I think that at three weeks old the kid would definately not need any heat, particularly in the summer! Any lambs I have that that are ill will be under a lamp for 2 maybe three days tops and that is during february when its seriously cold!
I would put the kid next to the older goats so it has company, it will really needs his own kind for company and to grow up well adjusted. After a week or so maybe you could try it with one of your quieter goats and see how they get on, as its a kid they will probably be more accepting than if it was an adult goat - presuming your goats know what kids are!