When you say your power supply is "3.5 Volts, 7.4mW and 2.11mA", what this means is that your power supply will provide 3.5V and a maximum current of 2.11mA (multiply both and you'll get its power). This means that you shouldn't connect it to something that'll draw more than 2.11mA at 3.5V: for example, a resistor of less than 1659 ohms. If you do, bad things will happen to the power supply (exactly which bad thing depends on your power supply).
So your wire must have a resistance of at least 1659 ohms. Lower than that and you could fry the power supply by demanding to much current. Much higher than that, though, and the current you'll draw will be much lower than 2.11mA, and so you'll get less power to heat your wire.
I can't really tell much more without details about your setup, but I can say that: if you want to achieve a high temperature in a wire with such a measly power supply, you are better off with thin wires of high resistance, because these will result in less metal (shorter and thinner wires) in order to get a 1659 ohm wire, and then you'll have less metal to heat with your 7.4mW of power.