82709

If we label each digit a, b, c, d and e, we get the following equations.
1. b + c = 9
2. a = b³
3. c + e = 16 (since 16 is the smallest number with five divisors – 1, 2, 4, 8 and 16).
4. d = 6 * d (The fourth and second-to-last digits are the same number, meaning d must be zero to satisfy the equation)
5. b must be zero, one or two (b can’t be three because that makes a=27, which isn’t a single digit). Zero and one result in duplicate digits (00907 and 11808 respectively) so the only remaining value for b is 2, giving us 82709 and warmth.