Re: 10,000 years ago, New York was buried under a sheet of ice 2 miles thick. The earth has been warming for the past 10,000 years.

there are two major causes of ice ages. The earth wobbles on it's
axis as it spins, in a 26,000 year cycle. Also, the sun varies in
it's intensity every so many thousands of years.

What causes ice-ages?

Fluctuations in the amount of insolation (incoming solar radiation)
are the most likely cause of large-scale changes in Earth's climate
during the Quaternary. In other words, variations in the intensity and
timing of heat from the sun are the most likely cause of the glacial/
interglacial cycles. This solar variable was neatly described by the
Serbian scientist, Milutin Milankovitch, in 1938. There are three
major components of the Earth's orbit about the sun that contribute to
changes in our climate. First, the Earth's spin on its axis is wobbly,
much like a spinning top that starts to wobble after it slows down.
This wobble amounts to a variation of up to 23.5 degrees to either
side of the axis. The amount of tilt in the Earth's rotation affects
the amount of sunlight striking the different parts of the globe. The
greater the tilt, the stronger the difference in seasons (i.e., more
tilt equals sharper differences between summer and winter
temperatures). The range of motion in the tilt (from left-of-center to
right-of-center and back again) takes place over a period of 41,000
years. As a result of a wobble in the Earth's spin, the position of
the Earth on its elliptical path changes, relative to the time of
year. This phenomenon is called the precession of equinoxes. The cycle
of equinox precession takes 23,000 years to complete. In the growth of
continental ice sheets, summer temperatures are probably more
important than winter.

How does the ice build up?

Throughout the Quaternary period, high latitude winters have been cold
enough to allow snow to accumulate. It is when the summers are cold,
(i.e., summers that occur when the sun is at its farthest point in
Earth's orbit), that the snows of previous winters do not melt
completely. When this process continues for centuries, ice sheets
begin to form. Finally, the shape of Earth's orbit also changes. At
one extreme, the orbit is more circular, so that each season receives
about the same amount of insolation. At the other extreme, the orbital
ellipse is stretched longer, exaggerating the differences between
seasons. The eccentricity of Earth's orbit also proceeds through a
long cycle, which takes 100,000 years. Major glacial events in the
Quaternary have coincided when the phases of axial tilt, precession of
equinoxes and eccentricity of orbit are all lined up to give the
northern hemisphere the least amount of summer insolation.

What makes the ice melt when the glaciation is over?

Major interglacial periods have occurred when the three factors line
up to give the northern hemisphere the greatest amount of summer
insolation. The last major convergence of factors giving us maximum
summer warmth occurred 11,000 years ago, at the transition between the
last glaciation and the current interglacial, the Holocene. During the
late Pleistocene, the Rocky Mountain regions of Canada and the regions
farther west were almost engulfed in the Cordilleran Ice Sheet, while
most of Canada east of the Rockies and the north-central and
northeastern United States were covered by the Laurentide Ice Sheet.
The divide between the two ice sheets lay east of the Rockies, with
the two ice bodies meeting near the U.S.-Canadian border in eastern
Montana. The Laurentide ice sheet is thought to have been as much as
two miles thick at the center.