When you mention that once the motor has been runing or that as the ambiant temp increases the motor becomes easier to start does suggest that the issue is glow plug related. You sayyou replaced the glow plugs which also suggests the issue is with the associated components in the glow plug system.
With these diesel engines, if there is fuel in the cylinder and tempreture to ignite the compressed fuel air mix then there is no reason why it will not run.
I recall a similar issue with a 2.8 hilux we had when i use to sell cars. Use google to find out how to diagnoise if your glow plug system is functioning correctly. You will be amazed at what sort of detailed info such as this that is available on the net. I found info on how to dianose faulty abs components, idle air contyoll, cruise controll and a heap of others over the years.