Robert,

There appears to be a bug in the way FindRoot handles units. I would report this.

This works:

In[1]:= FindRoot[Quantity[6, "ft"] == x, {x, Quantity[4, "in"]}]

Out[1]= {x -> Quantity[1.8288, "Meters"]}

but this does not:

In[6]:= FindRoot[
 Quantity[6, "ft"] == x, {x, Quantity[4, "in"], Quantity[400, "in"]}]

Out[6]= {x -> Quantity[10.16, ("Meters")^2]}

I generally avoid using units in expression handling as the results I've observed have been unpredictable. Your problem can be solved by doing this:

In[2]:= func[x_Real] := 
 QuantityMagnitude[
  ThermodynamicData["Water",  "Enthalpy", {"Pressure" -> p0, 
    "Temperature" -> Quantity[x, "DegreesFahrenheit"]}]]

In[11]:= FindRoot[QuantityMagnitude[h0] == func[tx], {tx, 900., 1100.}]

Out[11]= {tx -> 1000.}

Note that the x_Real pattern is necessary because I found that FindRoot calls the expression with symbols and numbers (I guess that it tries to first solve things analytically). If you do not protect the function by only letting it get called with Real numbers, you get the correct answer with warning messages like this:

ThermodynamicData::quant: tx is not a real number.

Regards