Plumbers putty removal

Heat will make the putty softer, which is why you can heat it up to remove it. Putty pretty much stays soft for years. Initially, it doesn't really dry out so much as oxidize which forms a skin on it.

If you absolutely must paint it right away, you'll probably has to use one of the latex based glazing compounds. If you want to use a traditional one, paint it as soon as it forms enough of a skin that the paint will stick to it. Also, I think you probably should be using oil based paints, but check the instructions on the putty.

If you let use know specifically which putty you are using, that might help get better answers.

Normally you can use latex over oil based products (never the other way around) if they are fully cured and dried. If the putty you are referring to is glazing compound, then you may have to wait a bit longer for it to cure. Glazing is very slow to cure and take paint. If you can still very easily dent it with your fingertip, wait, the solvents have not yet evaporated. You certainly can test a small area and see how it goes. However, don't be surprised if you get some peeling in a few months. Oil based paints are hard to find now, but would work better. I don't know what product you used, but there may be some recommendations on the can about painting.