Could it be that intermolecular forces in the para are lessened due to the location of the nitros?
Along the same lines as Bob Pursley suggested but with a slghtly different view, the ortho forms a 5-membered ring with the positive H of the OH and the negative O of the NO2 group. This is a strong INTRAmolecular force (within the same molecule). The p-nitrophenol is free to form the usual INTERmolecular bonds (H bonding between the OH of one molecule and the NO2 group of another molecule) which strengthens the crystal structure of the para isomer and that leads to a higher melting point for the para isomer. The ortho isomer lacks the forces between molecules that the para isomer has and it melts lower. My first year in grad school I was given a mixture of organic chemicals to separate and identify. o-nitrophenol was one of the compounds which I separated. It was near the end of the class period, I had to go to another class, I just put the solid on a piece of filter paper, placed it in my desk and went about my other classes. When I came back two days later to tackle the job of identification, ALL of it (and I do mean ALLLLL) was gone (it had completely volatilized) and I had to go through another 3-4 hours work to separate another batch. Tough lesson to learn BUT notice that the experience stayed me for the last 60 years and I remember to this day that o-nitrophenol is both smelly AND volatile. :-)