Comment by grues-dinner

Resistance is V/I. You literally cannot have current flowing in a resistor without a voltage across it (either the voltage causes the current to flow, or the resistor in the path of a flowing current has a voltage appear across it).

A voltage drop with a flowing current is power (P=VI).

There is literally nothing you can do to avoid resistors dissipating that power as heat, it's just what they are. If they didn't do it, they wouldn't be resistors.

What you can do is use larger resistances which need less current to see the same voltage (e.g. change a pull up from 10k to 100k or higher, but that's more sensitive to noise), or smaller resistances that drop less power from a given current (e.g. a miiliohm-range current shunt, and then you need a more sensitive input circuit) or find another way to do what you want (e.g. a switched-mode power supply is far more efficient than a voltage divider at stepping down voltage). This is usually much more complex and often requires fiddly active control, but is worth it in power-constrained applications, and with modern integrated technology, there's often a chip that does what you need "magically" for not much money.