Maybe try:

  f = FunctionInterpolation[QuantityMagnitude[
     ThermodynamicData["Water", 
      "Enthalpy", {"Pressure" -> Quantity[1.5*^7, "Pascals"], 
       "Temperature" -> Quantity[t, "Kelvins"]}]], {t,230,1000}]//Quiet

 FindRoot[f[t]== 1.4*^6, {t, 550.0, 610.0}]
 (*{t->584.113} *)

To avoid the error message "ThermodynamicData::quant: t is not a real number", we could use Quiet@FindRoot[...]

For a case like this: H(Temp) + b * Temp = c, we could define a function to calculate the enthalpy that only accepts numbers and thus avoid the first evaluation H[t] with t as a symbol, wich generates the error. For example:

H[Temp_Real] := 
 QuantityMagnitude[
  ThermodynamicData["Water", 
   "Enthalpy", {"Pressure" -> Quantity[P, "Pascals"], 
    "Temperature" -> Quantity[Temp, "Kelvins"]}]]

other form is

H[Temp_/;NumberQ@Temp]:=QuantityMagnitude[
      ThermodynamicData["Water", 
       "Enthalpy", {"Pressure" -> Quantity[P, "Pascals"], 
        "Temperature" -> Quantity[Temp, "Kelvins"]}]]

Pressure could also be included and tested in the H function.

As an example with the data you give

In[1]:=Clear[H, c]; 
H[Temp_Real] := 
 QuantityMagnitude[
  ThermodynamicData["Water", 
   "Enthalpy", {"Pressure" -> Quantity[1.5*^7, "Pascals"], 
    "Temperature" -> Quantity[Temp, "Kelvins"]}]];
c = H[584.113] + .1*584.113;
FindRoot[H[t] + .1*t == c, {t, 500.0, 610.0}] Out[1]:={t->584.113}