There may have been thunder early on the 28th, or the storms may have stayed a bit too far south.
Only 6 mornings had lows in the 30s F and two of those days dropped to 32 F. Of interest early in month was the morning low of 34 F here followed by an afternoon high at airport of 87 F on the 8th. A summary of heat records for the warmest Tucson March on record is available from the NWS at:
The first full week of April (today through 05:00 pm MST next Monday) starts out much like March. The GEFS temperature plumes for the week are above (note that there is a substantial cool bias in these models and the morning forecast from the NWS indicates high temperatures at the airport of 91 F on the 6th and 7th, before a cool front passes on the weekend. Gusty winds are indicated during a number of afternoons (just below).
The 00 UTC WRF-GFS forecast of precipitation for the coming week is shown at bottom. California's VERY wet cool season continues unabated over the northern half of the state, while dry conditions rule down here.