This happens in single player whether open to a LAN or not.

When you enter or exit the Nether Portal in survival, FPS drop and memory usage spikes to max. It takes several seconds after exiting the portal that FPS goes back to normal and memory usage drops.

It even happens if the chunks are already loaded on the other side of the portal by having someone already there.

This was also happening in the last couple of snapshots as well, but I'm not sure how far back it went. I didn't notice it happening in 1.8.8.

— Minecraft Crash Report ----
// Quite honestly, I wouldn't worry myself about that.

Time: 9/26/15 3:26 PM
Description: Exception in server tick loop

java.lang.OutOfMemoryError: Java heap space

A detailed walkthrough of the error, its code path and all known details is as follows:
---------------------------------------------------------------------------------------

– System Details –
Details:
Minecraft Version: 15w39c
Operating System: Windows 7 (amd64) version 6.1
Java Version: 1.8.0_31, Oracle Corporation
Java VM Version: Java HotSpot(TM) 64-Bit Server VM (mixed mode), Oracle Corporation
Memory: 4475496 bytes (4 MB) / 1060372480 bytes (1011 MB) up to 1060372480 bytes (1011 MB)
JVM Flags: 6 total; -XX:HeapDumpPath=MojangTricksIntelDriversForPerformance_javaw.exe_minecraft.exe.heapdump -Xmx1G -XX:+UseConcMarkSweepGC -XX:+CMSIncrementalMode -XX:-UseAdaptiveSizePolicy -Xmn128M
IntCache: cache: 0, tcache: 0, allocated: 12, tallocated: 94
Profiler Position: N/A (disabled)
Player Count: 2 / 8; [lm['Aniline_Selenic'/593621, l='Dragon Islands', x=50.70, y=81.02, z=274.70], lm['Falenore'/595365, l='Dragon Islands', x=34.50, y=77.00, z=286.12]]
Type: Integrated Server (map_client.txt)
Is Modded: Probably not. Jar signature remains and both client + server brands are untouched.