[Igor (OP)]

What is the time interval between the daylight minimum, (i.e. the shortest day),
and the temperature minimum ?

Is this delay latitude dependant ?, (e.g. does it differ in different countries ?).

[another_someone]

It would depend on cloud cover, and most importantly, in coastal localities the effects of the sea are very important.

[JimBob]

Also important, and where I live, somewhat more important, is the ground cover. Asphalt and concrete makes a cit very much a heat sink. This means it gets hotter during the day and that cooling is MUCH slower at night.

The amount of trees also causes differences - in the shade the ground does not get as warm. Believe it or not, it is cooler below the surface of the Sahara desert than at an equivalent latitude in coastal Mexico. The radiational shedding of heat in the Sahara  allows for cooler beneath the surface.

Central Mexico is in general, a little cooler than the coast because of altitude and abundant ground cover.

[Bass]

From experience in Montana, the delay is probably in the order of 2 weeks to a month.  Mid January is our coldest time of year, and July our hottest.  My thought is that the lag is due to the delay of the earth's surface to warm or cool after the summer/winter solstice- my guess is that the lag would be greater at higher latitudes, but probably also affected by local geography (nearby water, mountains, etc.)