Safe temperature thresholds for #2 HDPE and #5 PP plastic

Generally I would recommend against heating a plastic container with a resistance heater (like a hot plate or mug warmer) unless you know for a fact it has a hardware shutoff that will kick in well below the melting point. Hardware failures do happen, and I've personally seen a runaway hot plate almost melt an unattended plastic container (full of alcohol!).

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That being said, it depends on your risk tolerance. Generally I avoid heating food or drink in containers not designed to be heated. Even if they are labeled BPA-free, some manufacturers have simply switched to using other bisphenols like bisphenol S (BPS), which apparently act in the body in a similar way to BPA but are chemically distinct, allowing the manufacturers to still use the BPA-free label. To be fair, BPS seems to be a bit more heat-stable than BPA, but still. I would bet that even some plastic products designed for heating food in have this issue.

All that said, there's not much you can do to get away from endocrine disruptors entirely. Even if you managed to avoid all plastic in the kitchen, they're just in the environment at this point. So given that you are already being exposed to them, whether you want to be concerned about ingesting some more by heating your food in plastic containers is up to you. If it's much more convenient and you don't care that much, go for it. If you're concerned about the health implications and it would only save you a bit of effort, probably not worth it.

Finally, I'm not an expert nor a doctor$-$I would advise doing some research on the health effects yourself, since I can't really speak to those with any more authority than Wikipedia.