First, why would the glue not be the same temperature as the water unless you're incredibly impatient?
And second, why not use a candy thermometer just to make sure of the temperature? The Rival hot pots are notoriously all over the map as far as temperature is concerned...I wouldn't trust one without using a thermometer.
We use a traditional hot hide glue pot, but use the 3 oz. plastic squeeze jar technique. Water in the glue pot, glue bottles in the water. We fire up the glue pot in the morning and just leave it going all day. No issues re. temperature, though I did have to rewire the thing at one point and recalibrate it.
And, yes, runny like maple syrup...but that does not tell you the temperature. You can adjust viscosity via temperature or by how much water you put in there. You could have very runny hot hide glue at 100 F. if it were thinned out too much. And is that hot maple syrup or cold? You should have one known constant...the temperature...and that will cost you all of about 8 bucks to check.
Iffy glue joints are not something to screw around with. Do it right, get it right, and then you won't have to worry.