there still is a
flow shutoff valve attached to the air conditioner/heat pump that is
operated by a solenoid. The solenoid is normally energized but the
voltage suppied to it exceeds the normal recommended operating voltage
and gets very hot. The unit is an ALCO Controls, Coil Type DMG, 24
volts, 7 watts, 50 - 60 Hz. The computer in the furnace is supplying 26
to 28 volts.

What I would like to do is attach a power resistor to reduce the
voltage. The assumption I would like to make is the highest voltage to
the solenoid would be 30 volts. The solenoid will activate at as low of
a voltage as 17 volts. I would like to add a resistor that will take
the 30 volts and reduce the voltage to 24 volts.

How do I go about computing the value for the resistor? Is there a
better way of going about this than using a resistor?

The solenoid coil is not a resistance, it is an impedance composed of
orthogonal resistive and reactive parts, and this impedance is a strong
function of whether the solenoid is in or out, varying over a 2-3 range.
Placing a resistor in series may very well blow the transformer
because the resistor presents too much drop at "inrush" and the solenoid
hangs at a current loading in excess of the transformer VA.
http://www.radiofrigor.com.br/download/coils.pdf
Your line readings are suspect and unreliable. You don't make it clear
about the solenoid being permanently on or not, , thinking it more
important to tell us totally irrelevant things like it is in a house
belonging to your mother's boyfriend. If this is the kind of thing you
focus on, then stay away from the furnace.