In order to distinguish hail from a thunderstorm you should know how the temperature is decreasing with altitude. Generally if it decreases really fast you have formation of hail. (Edit: you mentioned dew point, this is where condensation of warm hair happens, freezing level is not the same thing and it will be located somewhere higher than the dew point. Knowing the Dry Adiabatic Lapse Rate and the Saturated Adiabatic Lapse Rate is necessary to find cloudbase and freezing level. Im not sure how much in depth you want to go with these things so I will let you do the research on it. A pilot course booklet will have a simple explanation of the whole thing) Where I'm from this happens and hail is fairly common in certain periods of the year, so season becomes one of the indications in those cases.
Dry air at a certain altitude will lower the freezing level in the atmosphere, a lower freezing level means that eventual hail wont have the time to melt into drops like it would if it had to fall longer through a warmer air layer. For the same reason places at higher altitudes would be closer to the normal freezing level. I don't think you can know how dry is the air at a certain altitude with a simple weather station that gets datas only from ground level. What you know, though, is that certain places tend to often have this dry middle layer and so location becomes an indicator for you as those are informations you can find.
Wind, higher up, that you can more or less tell from looking at the clouds before the event and around (movement and plumes). In a thunderstorm you have strong updrafts and downdrafts, if vertical and in all directions (that, I guess, you would know collecting live datas from various weather stations in the region if you want to use want to use only simple datas) you tend to have a short or failed thunderstorm but if there is high wind higher up (speed wind shear where higher altitude winds are much faster than ground levels) you find that it can push the updraft sideways (updraft and downdraft will form a sort of Λ ) so that the feed of warmer hair is maintained and the updraft speed (Upward Vertical Velocity, if you want to look it up on your own) will be high and hail and violent thunderstorms (or worse) can result between updraft and downdraft.
Also, where I'm from, farmers look at storm clouds approaching and if these present lighter streaks they know hail is coming (and you used to start hearing hail cannons). For this reasons clouds become another indication, with short notice though. Once I started paragliding, skydiving and kayaking weather forecast and satellite datas became much more important and reliable than anything else to figure out possibilities of hail storms much earlier.
So if where you live the weather is so unpredictable to not match anything above there wont be much simple datas you can collect yourself at ground level that will give much notice. If you want to collect weather informations available on the net to make your own forecasts you obviously can, learning a bit of meteorology, but at that point you find the forecasts already prepared for you and probably more reliable.
PS: with the data you listed alone, no you can't tell what’s gonna come down.