I would second the sliding fit and use Loctite 641 bearing fit or its equivalent.
A 0.001" interference on a 3/8" diameter is very high, we used to reckon on 0.001" per inch of diameter as a good interference fit.
Heating one part and cooling the other works well on parts that have a reasonable mass, but small components will equalise their temperature too quickly and you may not get them together before they grab.
With a small diameter bush like this, probably with a thin wall thickness, nearly all the interference will end up reducing the bore. With the Loctite method the bush can be finished to size before fitting.
How much clearance? Check the data sheet for what you have. Loctite guide gives 0.001 to 0.003 clearance as optimum.
Neil
Edited By Neil A on 06/03/2019 21:58:06
Edited By Neil A on 06/03/2019 22:08:35