To further answer your question, I think it would be easier to import everything, then do a bit of manipulation on the columns. I'm not sure why you want to remove the temperature units, I'd just convert these to a Quantity and preserve the unit value. This works fine with TimeSeries/DateListPlot:
hwd = Import["hw.tsv", "Data", "HeaderLines" -> 1];
hwd = MapAt[DateObject[StringReplace[#, " GMT +0" -> ""]] &, hwd, {All, 1}];
hwd = MapAt[Quantity, hwd, {All, 2}];
ts = TimeSeries[hwd]
DateListPlot[ts]
If you really want to remove the units, change the third line to :
hwd = MapAt[ToExpression[StringReplace[#, " " ~~ __ -> ""]] &, hwd, {All, 2}];