Hello,
generally no chemicals at all should contact any container, glas, bottle or other equipment which is intended for food. Heating is only necessary up to about 50-60° C for quicker dissolution of chemicals. The best way is to buy a small magnetic stirrer with controlled heating. Look for a used one on e-bay, it is quite useful for preparing all photographic solutions. TEA is not very toxic and is used even in cosmetic formulations for direct skin contact. It has a high flash point and high boiling point.
When making glycol or TEA based developers it is not necessary to heat the solvents(s). Doing so only hastens decomposition of the developing agents. Everything will dissolve if one is patient. Chemicals should never be brought into areas where food is eaten or prepared.
No. I use a Pyrex glass measuring jug standing in a pan of water that is heated on the stove top using a thermometer to gently stir it and to watch as the temperature gets to 65 degrees Celsius at which I then dissolve the ingredients for 510-PYRO. I make 400ml at a time and bottle it in two 200ml bottles. It lasts indefinitely even though I heated the TEA and it develops exactly as I want it to. I do keep the jug and pan just for this job and there is no food around when I work in the kitchen.
Or, you could just use hot tap water to heat the solution a bit, using the water-bath technique that Rod mentions above. That would get you to 45°C or so easily and likely speed things up a bit.
What I did was to mix all the ingredients in the intended storage bottle and then over the course of the next few minutes would invert the bottle several times. During this time there are many other things that you can do.