Cover the icy pole with a continent, and the other pole with open ocean. Make the planet about $20^\circ C$ warmer than the Earth.
Oceans are great temperature distributors, bringing relatively warm water to what would otherwise be far colder climates. Because of this, a pole with an ocean on it is going to be significantly warmer than a pole covered by a land mass. On Earth, the North Pole fluctuates between $20^\circ C$ ($36^\circ F$) and $30^\circ C$ ($54^\circ F$) warmer than the South Pole, depending on the time of year, with the difference most pronounced in the Summer.
On an Earth-like planet which was around $20^\circ C$ ($36^\circ F$) warmer, the south pole would remain below freezing year round, retaining an ice cap, while the ice cap covering the North Pole would rise significantly above freezing and melt during the summer. Ice caps have a much higher albedo than open ocean, which is good at absorbing heat, so it's likely that without a summer ice cap, the difference in polar temperatures would be even greater than what we see on Earth.
Wider ocean channels between the equatorial oceans and your polar sea would also increase polar temperatures, On Earth, the Arctic Ocean is largely ringed by land, which helps the ocean stay cold by limiting the degree to which it exchanges water with warmer oceans. Arctic regions on Earth which are more open to currents from the south have less ice than those which are more landlocked, with open ocean stretching as far north as Svalbard, even in the winter, while the Northern cost of Alaska remains ice bound year round, despite being significantly further south. The further warm ocean currents from the south are able to penetrate your polar ocean, the more difficult it will be for that ocean to form a cap of sea ice.