Sunshine can cause temperatures inside a greenhouse or polytunnel to soar. If there is no natural shading for the greenhouse then you may need to apply shading of some sort. June is also often a dry month and so one major task will be ensuring that your plot is watered. You need to prioritise which plants need most water such as seedlings, new plantings etc.
Unfortunately the improved conditions are also enjoyed by weeds.
For a list of suggested tasks for June click here. Please add any suggestions that I may have overlooked in the comments here.