Indeed, there was a 31 day spell, from I think 22nd July 1995 to 21st August 1995, when the average daily maximum at my place of work at Carne near Portadown, Co. Armagh, was 26.4 deg. C. (non-standard exposure and thermometer, probably 1-2 deg. C. too high). The rainfall for August 1995 was 4.4 mm, which is also easily the lowest of any 31 day period since
I began measuring rainfall, etc, in late May 1995; the rainfall for July 1995 was I think 47.4 mm and for June 21.0 mm. Most of Julys rainfall was in the 1st half, but as the longest rainless spell of 1995 was a mere 13 days from 29th July to 10th August (half that from 28th August to 22nd September in the next year, 1996, which was the longest), clearly there was rain on 28th July, so the rainfall from 22nd July to 21st August was at least a little higher than 1st-31st August.
I do not have figures for sunshine, but it was certainly very sunny (August, though not quite as sunny in Northern Ireland as in August 1947 with 261.6 and 1976 with 254.6 hours, was still the 3rd sunniest on record with 232.9 hours). I believe daily sunshine values of 9.15 hours/day (283.8 hours) were recorded at Silent Valley, Co. Down, though the sunniest summer was 7.73 hours/day (711.2 hours) at Newtownards, Co. Down, equalling that of Rosslare, Co. Wexford in 1995, which I think may also have had its sunniest summer on record (and it is normally rather sunnier than north-east Ireland).
No comparable 4 week period (for warmth) has occurred since (even in July-August 2003, July 2006, etc). The warmest day during that period at Carne was 31.5 deg. C. on 20th August, I think (though the highest I have recorded there was 32.0 deg. C. on 29th June 1995; 30 deg. C. or more has been recorded in several subsequent years including 1997, 1999, 2003, 2005 and 2006), although the official highest temperature in Northern Ireland during the summer of 1995 was 30.6 deg. C. at Ballylisk near Tandragee, Co. Armagh (about 5 miles away) on 2nd August; this is the highest temperature recorded in Northern Ireland in August, and within 0.2 deg. C. of the official highest temperatures for Northern Ireland of 30.8 deg. C. on 30th June 1976 (Knockarevan near Garrison, Co. Fermanagh) and 12th July 1983 (Shaws Bridge near Belfast, Co. Down/Antrim). Unfortunately the Ballylisk station (which often had some of the highest temperatures in Co. Armagh, including the previous highest August value of 29.7 deg. C. on 3rd August 1975) closed down a few years later, so I have no close station for comparison.