I need to regulate the temperature of a vial between 40 to 80 degrees Celsius, allowing the user to select the desired temperature. I'm unsure which heating element to use. After some research, I've found that a Peltier element could be an ideal choice. Is this the best option, or are there better alternatives for this application?
I don't think there is a one-size-fits-all best way to heat "a vial". I feel like the best answer will depend on the size and material and heat capacity of what is in it. It will depend on the initial temp and how fast you want it to change. Are you maintaining temp or heating something? There are a LOT of details that will go into choosing the best idea. You can't just assume that all vials of stuff are the same.
If the temperature is supposed to be uniform throughout the vial, it needs to be in an insulated box, with the interior held at some uniform temperature. The heating element required will depend on the details of the insulated box.
What response time is allowed for the heating. You mentioned the worst possible source of controlled heat, so are you also needing cooling?
For a small heater at a relatively low temperature, I'd use a large (physically large) resistor. Probably around 1-5W rating.
Peltier's a heat pump and typically only used if you also need cooling.