I have a similar cabinet with same problems too.

My cab is 2Lx4Wx5H with a total of 40 cubic feet with a bathroom fan rated at 70 CFM thats connected to 3in tubing, I have two passive intakes which are grills cut into the back of the cab.

My lamp is a 250w HPS

same probblem as kind67 the temp for my cab jumps almost to 90F when i turn on my HPS, I have been keeping my seedlings under two T5 2ft 24 watt and one 20w 2ft fluoro.

the room the cab is in stays around 75-80 but the cab jumps almost to 90. i know i defnitely need a better fan, im not sure rated for how much CFM. i was wondering if there are any other tips for keeping the temp down or how much should i get my new fan?